Maximal regularity and global existence of solutions  to a quasilinear  thermoelastic plate  system

Irena Lasiecka; Mathias Wilke

doi:10.3934/dcds.2013.33.5189

Previous Article
Stability estimates for semigroups on Banach spaces
DCDS Home
This Issue
Next Article
Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach

November 2013, 33(11&12): 5189-5202. doi: 10.3934/dcds.2013.33.5189

Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system

Irena Lasiecka ^1, and Mathias Wilke ^2,

1.	Department of Mathematics, University of Virginia, Charlottesville, VA 22903
2.	Institut für Mathematik, Martin-Luther Universität Halle-Wittenberg, 06099 Halle

Received November 2011 Revised October 2012 Published May 2013

Abstract
Related Papers

We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in $\mathbb{R}^n$. Global Well-posedness of solutions is shown by applying the theory of maximal parabolic regularity of type $L_p$. In addition, we prove exponential decay rates for strong solutions and their derivatives.

Keywords: existence and uniqueness of strong solutions, maximal regularity, Quasilinear thermoelastic plates, exponential decay..

Mathematics Subject Classification: Primary: 74F05; Secondary: 35B30, 35B40, 74H4.

Citation: Irena Lasiecka, Mathias Wilke. Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5189-5202. doi: 10.3934/dcds.2013.33.5189

References:

[1]	S. A. Ambartsumian, M. V. Belubekyan and M. M. Minasyan, On the problem of vibrations of nonlinear elastic electroconductive plates in transverse and longitudinal magnetic fields,, International Journal of Nonlinear Mechanics, 19 (1983), 141. Google Scholar
[2]	P. Acquistapace and B. Terreni, Some existence and regularity results for abstract non-autonomous parabolic equations,, Journal of Mathematical Analysis and Applications, 99 (1984), 9. doi: 10.1016/0022-247X(84)90234-8. Google Scholar
[3]	S. Angenent, Nonlinear analytic semiflows,, Proc. Roy. Soc. Edinburgh Sect. A, 115 (1990), 91. doi: 10.1017/S0308210500024598. Google Scholar
[4]	G. Avalos and I. Lasiecka, Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation,, SIAM Journal of Mathematical Analysis, 29 (1998), 155. doi: 10.1137/S0036141096300823. Google Scholar
[5]	G. Avalos and I. Lasiecka, Exponential stability of a thermoelastic system without dissipation,, Rend. Istit. Mat. Univ. Trieste, XXVIII (1997), 1. Google Scholar
[6]	G. Avalos and I. Lasiecka, On the null-controllability of thermoelastic plates and singularity of the associated minimal energy function,, Journal of Mathematical Analysis and its Applications, 10 (2004), 34. doi: 10.1016/j.jmaa.2004.01.035. Google Scholar
[7]	G. Avalos and I. Lasiecka, Uniform decays in nonlinear thermoelasticity,, in, 15 (1998), 1. Google Scholar
[8]	A. Benabdallah and M. G. Naso, Nullcontrolability of thermoelastic plates,, Abstract and Applied Analysis, 7 (2002), 585. doi: 10.1155/S108533750220408X. Google Scholar
[9]	G. Y. Bagdasaryan, "Vibrations and Stability of Magnetoelastic Systems,", Yerevan, (1999). Google Scholar
[10]	C. Dafermos, On the existence and asymptotic stability of solutions to the equations of nonlinear thermoelasticity,, Arch. Rat. Mechanics. Anal., 29 (1968), 241. doi: 10.1007/BF00276727. Google Scholar
[11]	C. Dafermos and L. Hsiao, Development of singularities in solutions of the equations of nonlinear thermoelasticity,, Quart. Appl. Math., 44 (1986), 463. Google Scholar
[12]	G. Da Prato and P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation,, Journal of Functional Analysis, 58 (1984), 107. doi: 10.1016/0022-1236(84)90034-X. Google Scholar
[13]	K. Deimling, "Nonlinear Functional Analysis,", Springer, (1985). Google Scholar
[14]	R. Denk, M. Hieber and J. Prüss, $\mathcalR$-boundedness, Fourier Multipliers and Problems of elliptic and parabolic type,, Memoirs of the AMS, (2003). Google Scholar
[15]	R. Denk and R. Racke, $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations,, Electronic Journal of Differential Equations, (2006). Google Scholar
[16]	R. Denk, Y. Shibata and R. Racke, $L^p$ theory for the linear thermoelastic plate equations in bounded and exterior domains,, Konstanzer Schriften in Mathematik und Informatik, 240 (2008). Google Scholar
[17]	M. Eller, I. Lasiecka and R. Triggiani, Simultaneous exact-approximate boundary controllability of thermo-elastic plates with variable thermal coefficients and moment control,, Journal of Mathematical Analysis and its Applications, 251 (2000), 452. doi: 10.1006/jmaa.2000.7015. Google Scholar
[18]	M. Eller, I. Lasiecka and R. Triggiani, Unique continuation result for thermoelastic plates,, Inverse and Ill-Posed Problems, 9 (2001), 109. Google Scholar
[19]	D. Hasanyan, N. Hovakimyan, A. J. Sasane and V. Stepanyan, Analysis of nonlinear thermoelastic plate equations,, in, 2 (2004), 1514. doi: 10.1109/CDC.2004.1430258. Google Scholar
[20]	S. Hansen and B. Zhang, Boundary control of a linear thermoelastic beam,, Journal of Mathematical Analysis and its Applications, 210 (1997), 182. doi: 10.1006/jmaa.1997.5437. Google Scholar
[21]	S. Hansen, Exponential decay in a linear thermoelastic rod,, J. Math. Anal. Appl., 187 (1992), 428. doi: 10.1016/0022-247X(92)90217-2. Google Scholar
[22]	A. A. Ilyushin, "Plasticity. Part One. Elasticity-Plastic Deformations,", OGIZ, (1948). Google Scholar
[23]	S. Jiang and R. Racke, "Evolution Equations in Thermoelasticity,", Chapman and Hall, (2000). Google Scholar
[24]	J. U. Kim, On the energy decay of a linear thermoelastic bar and plate,, SIAM Journal of Mathematical Analysis, 23 (1992), 889. doi: 10.1137/0523047. Google Scholar
[25]	H. Koch and I.Lasiecka, Backward uniqueness in linear thermo-elasticity with variable coefficients,, Functional Analysis and Evolution Equations, (2007). Google Scholar
[26]	M. Köhne, J. Prüss and M. Wilke, On quasilinear parabolic evolution equations in wheighted $L_p$-spaces,, J. Evol. Equ., 10 (2010), 443. doi: 10.1007/s00028-010-0056-0. Google Scholar
[27]	J.Lagnese, The reachability problem for thermoelastic plates,, Archive for Rational Mechanics and Analysis, 112 (1990), 223. doi: 10.1007/BF00381235. Google Scholar
[28]	J. Lagnese, "Boundary Stabilization of Thin Plates,", SIAM, (1989). doi: 10.1137/1.9781611970821. Google Scholar
[29]	I. Lasiecka, Uniform decay rates for full von Karman system of dynamic thermoelasticity with free boundary conditions and partial boundary dissipation,, Communications in Partial Differential Equations, 24 (1999), 1801. doi: 10.1080/03605309908821483. Google Scholar
[30]	I. Lasiecka and C. Lebiedzik, Asymptotic behavior of nonlinear structural acoustic interactions with thermal effects on the interface,, Nonlinear Analysis, 49 (2002), 703. doi: 10.1016/S0362-546X(01)00135-3. Google Scholar
[31]	I. Lasiecka and C. Lebiedzik, Boundary stabilizability of nonlinear structural acoustic models with thermal effects on the interface,, C.R. Acad. Sci. Paris, 328 (2000), 187. doi: 10.1016/S1287-4620(00)00111-3. Google Scholar
[32]	I. Lasiecka, S. Maad and A. Sasane, Existence and exponential decay of solutions to a quasilinear thermoelastic plate system,, NODEA, 15 (2008), 689. doi: 10.1007/s00030-008-0011-8. Google Scholar
[33]	I. Lasiecka and T. Seidman, Blowup estimates for observability of a thermoelastic system,, Asymptotic Analysis, 50 (2006), 93. Google Scholar
[34]	I. Lasiecka and R. Triggiani, Structural decomposition of thermoelastic semigroups with rotational forces,, Semigroup Forum, 60 (2000), 16. doi: 10.1007/s002330010003. Google Scholar
[35]	I. Lasiecka and R. Triggiani, "Control Theory for PDEs,", Cambridge University Press, 1 (2000). Google Scholar
[36]	I. Lasiecka, M. Renardy and R. Triggiani, Backward uniqueness of thermoelastic plates with rotational forces,, Semigroup Forum, 62 (2001), 217. doi: 10.1007/s002330010035. Google Scholar
[37]	I. Lasiecka and R. Triggiani, Exact null-controllability of structurally damped and thermoelastic parabolic models,, Rend. Mat. Acta Lincei, 9 (1998), 43. Google Scholar
[38]	I. Lasiecka and R. Triggiani, Analyticity, and lack thereof, of thermoelastic semigroups,, European Series in Applied and Industrial Mathematics, 4 (1998), 199. doi: 10.1051/proc:1998029. Google Scholar
[39]	L. Librescu, "Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-type Structures,", Noordhoff, (1975). doi: 10.1115/1.3423921. Google Scholar
[40]	L. Librescu, D. Hasanyan, Z. Qin and D. Ambur, Nonlinear magnetothermoelasticity of anisotropic plates in a magnetic field,, Journal of Thermal Stresses, 26 (2003), 1277. doi: 10.1080/714050886. Google Scholar
[41]	Z. Liu and M. Renardy, A note on the equation of a thermoelastic plate,, Appl. Math. Letters, 8 (1995), 1. doi: 10.1016/0893-9659(95)00020-Q. Google Scholar
[42]	A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems,", Birkhauser, (1995). doi: 10.1007/978-3-0348-9234-6. Google Scholar
[43]	A. Lunardi, Abstract quasilinear parabolic equations,, Math. Ann., 267 (1984), 395. doi: 10.1007/BF01456097. Google Scholar
[44]	A. Lunardi, Global solutions of abstract quasilinear parabolic equations,, Journal Differential Equations, 58 (1985), 228. doi: 10.1016/0022-0396(85)90014-2. Google Scholar
[45]	A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", Applied Mathematical Sciences, 44 (1983). doi: 10.1007/978-1-4612-5561-1. Google Scholar
[46]	J. Prüss, Maximal regularity for evolution equations in $L_p$-spaces,, Conf. Semin. Mat. Univ. Bari, (2002), 1. Google Scholar
[47]	J. Prüss and G. Simonett, Maximal regularity for evolution equations in weighted $L_p$-spaces,, Arch. Math., 82 (2004), 415. doi: 10.1007/s00013-004-0585-2. Google Scholar
[48]	J. E. Muñoz Rivera and R. Racke, Smoothing properties, decay, and global existence of solutions to nonlinear coupled systems of thermoelastic type,, SIAM Journal on Mathematical Analysis, 26 (1995), 1547. doi: 10.1137/S0036142993255058. Google Scholar
[49]	J. E. Muñoz Rivera and R. Racke, Large solutions and smoothing properties for nonlinear thermoelastic systems,, Journal of Differential Equations, 127 (1996), 454. doi: 10.1006/jdeq.1996.0078. Google Scholar
[50]	H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators,", North-Holland, (1978). Google Scholar

show all references

References:

[1]	S. A. Ambartsumian, M. V. Belubekyan and M. M. Minasyan, On the problem of vibrations of nonlinear elastic electroconductive plates in transverse and longitudinal magnetic fields,, International Journal of Nonlinear Mechanics, 19 (1983), 141. Google Scholar
[2]	P. Acquistapace and B. Terreni, Some existence and regularity results for abstract non-autonomous parabolic equations,, Journal of Mathematical Analysis and Applications, 99 (1984), 9. doi: 10.1016/0022-247X(84)90234-8. Google Scholar
[3]	S. Angenent, Nonlinear analytic semiflows,, Proc. Roy. Soc. Edinburgh Sect. A, 115 (1990), 91. doi: 10.1017/S0308210500024598. Google Scholar
[4]	G. Avalos and I. Lasiecka, Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation,, SIAM Journal of Mathematical Analysis, 29 (1998), 155. doi: 10.1137/S0036141096300823. Google Scholar
[5]	G. Avalos and I. Lasiecka, Exponential stability of a thermoelastic system without dissipation,, Rend. Istit. Mat. Univ. Trieste, XXVIII (1997), 1. Google Scholar
[6]	G. Avalos and I. Lasiecka, On the null-controllability of thermoelastic plates and singularity of the associated minimal energy function,, Journal of Mathematical Analysis and its Applications, 10 (2004), 34. doi: 10.1016/j.jmaa.2004.01.035. Google Scholar
[7]	G. Avalos and I. Lasiecka, Uniform decays in nonlinear thermoelasticity,, in, 15 (1998), 1. Google Scholar
[8]	A. Benabdallah and M. G. Naso, Nullcontrolability of thermoelastic plates,, Abstract and Applied Analysis, 7 (2002), 585. doi: 10.1155/S108533750220408X. Google Scholar
[9]	G. Y. Bagdasaryan, "Vibrations and Stability of Magnetoelastic Systems,", Yerevan, (1999). Google Scholar
[10]	C. Dafermos, On the existence and asymptotic stability of solutions to the equations of nonlinear thermoelasticity,, Arch. Rat. Mechanics. Anal., 29 (1968), 241. doi: 10.1007/BF00276727. Google Scholar
[11]	C. Dafermos and L. Hsiao, Development of singularities in solutions of the equations of nonlinear thermoelasticity,, Quart. Appl. Math., 44 (1986), 463. Google Scholar
[12]	G. Da Prato and P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation,, Journal of Functional Analysis, 58 (1984), 107. doi: 10.1016/0022-1236(84)90034-X. Google Scholar
[13]	K. Deimling, "Nonlinear Functional Analysis,", Springer, (1985). Google Scholar
[14]	R. Denk, M. Hieber and J. Prüss, $\mathcalR$-boundedness, Fourier Multipliers and Problems of elliptic and parabolic type,, Memoirs of the AMS, (2003). Google Scholar
[15]	R. Denk and R. Racke, $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations,, Electronic Journal of Differential Equations, (2006). Google Scholar
[16]	R. Denk, Y. Shibata and R. Racke, $L^p$ theory for the linear thermoelastic plate equations in bounded and exterior domains,, Konstanzer Schriften in Mathematik und Informatik, 240 (2008). Google Scholar
[17]	M. Eller, I. Lasiecka and R. Triggiani, Simultaneous exact-approximate boundary controllability of thermo-elastic plates with variable thermal coefficients and moment control,, Journal of Mathematical Analysis and its Applications, 251 (2000), 452. doi: 10.1006/jmaa.2000.7015. Google Scholar
[18]	M. Eller, I. Lasiecka and R. Triggiani, Unique continuation result for thermoelastic plates,, Inverse and Ill-Posed Problems, 9 (2001), 109. Google Scholar
[19]	D. Hasanyan, N. Hovakimyan, A. J. Sasane and V. Stepanyan, Analysis of nonlinear thermoelastic plate equations,, in, 2 (2004), 1514. doi: 10.1109/CDC.2004.1430258. Google Scholar
[20]	S. Hansen and B. Zhang, Boundary control of a linear thermoelastic beam,, Journal of Mathematical Analysis and its Applications, 210 (1997), 182. doi: 10.1006/jmaa.1997.5437. Google Scholar
[21]	S. Hansen, Exponential decay in a linear thermoelastic rod,, J. Math. Anal. Appl., 187 (1992), 428. doi: 10.1016/0022-247X(92)90217-2. Google Scholar
[22]	A. A. Ilyushin, "Plasticity. Part One. Elasticity-Plastic Deformations,", OGIZ, (1948). Google Scholar
[23]	S. Jiang and R. Racke, "Evolution Equations in Thermoelasticity,", Chapman and Hall, (2000). Google Scholar
[24]	J. U. Kim, On the energy decay of a linear thermoelastic bar and plate,, SIAM Journal of Mathematical Analysis, 23 (1992), 889. doi: 10.1137/0523047. Google Scholar
[25]	H. Koch and I.Lasiecka, Backward uniqueness in linear thermo-elasticity with variable coefficients,, Functional Analysis and Evolution Equations, (2007). Google Scholar
[26]	M. Köhne, J. Prüss and M. Wilke, On quasilinear parabolic evolution equations in wheighted $L_p$-spaces,, J. Evol. Equ., 10 (2010), 443. doi: 10.1007/s00028-010-0056-0. Google Scholar
[27]	J.Lagnese, The reachability problem for thermoelastic plates,, Archive for Rational Mechanics and Analysis, 112 (1990), 223. doi: 10.1007/BF00381235. Google Scholar
[28]	J. Lagnese, "Boundary Stabilization of Thin Plates,", SIAM, (1989). doi: 10.1137/1.9781611970821. Google Scholar
[29]	I. Lasiecka, Uniform decay rates for full von Karman system of dynamic thermoelasticity with free boundary conditions and partial boundary dissipation,, Communications in Partial Differential Equations, 24 (1999), 1801. doi: 10.1080/03605309908821483. Google Scholar
[30]	I. Lasiecka and C. Lebiedzik, Asymptotic behavior of nonlinear structural acoustic interactions with thermal effects on the interface,, Nonlinear Analysis, 49 (2002), 703. doi: 10.1016/S0362-546X(01)00135-3. Google Scholar
[31]	I. Lasiecka and C. Lebiedzik, Boundary stabilizability of nonlinear structural acoustic models with thermal effects on the interface,, C.R. Acad. Sci. Paris, 328 (2000), 187. doi: 10.1016/S1287-4620(00)00111-3. Google Scholar
[32]	I. Lasiecka, S. Maad and A. Sasane, Existence and exponential decay of solutions to a quasilinear thermoelastic plate system,, NODEA, 15 (2008), 689. doi: 10.1007/s00030-008-0011-8. Google Scholar
[33]	I. Lasiecka and T. Seidman, Blowup estimates for observability of a thermoelastic system,, Asymptotic Analysis, 50 (2006), 93. Google Scholar
[34]	I. Lasiecka and R. Triggiani, Structural decomposition of thermoelastic semigroups with rotational forces,, Semigroup Forum, 60 (2000), 16. doi: 10.1007/s002330010003. Google Scholar
[35]	I. Lasiecka and R. Triggiani, "Control Theory for PDEs,", Cambridge University Press, 1 (2000). Google Scholar
[36]	I. Lasiecka, M. Renardy and R. Triggiani, Backward uniqueness of thermoelastic plates with rotational forces,, Semigroup Forum, 62 (2001), 217. doi: 10.1007/s002330010035. Google Scholar
[37]	I. Lasiecka and R. Triggiani, Exact null-controllability of structurally damped and thermoelastic parabolic models,, Rend. Mat. Acta Lincei, 9 (1998), 43. Google Scholar
[38]	I. Lasiecka and R. Triggiani, Analyticity, and lack thereof, of thermoelastic semigroups,, European Series in Applied and Industrial Mathematics, 4 (1998), 199. doi: 10.1051/proc:1998029. Google Scholar
[39]	L. Librescu, "Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-type Structures,", Noordhoff, (1975). doi: 10.1115/1.3423921. Google Scholar
[40]	L. Librescu, D. Hasanyan, Z. Qin and D. Ambur, Nonlinear magnetothermoelasticity of anisotropic plates in a magnetic field,, Journal of Thermal Stresses, 26 (2003), 1277. doi: 10.1080/714050886. Google Scholar
[41]	Z. Liu and M. Renardy, A note on the equation of a thermoelastic plate,, Appl. Math. Letters, 8 (1995), 1. doi: 10.1016/0893-9659(95)00020-Q. Google Scholar
[42]	A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems,", Birkhauser, (1995). doi: 10.1007/978-3-0348-9234-6. Google Scholar
[43]	A. Lunardi, Abstract quasilinear parabolic equations,, Math. Ann., 267 (1984), 395. doi: 10.1007/BF01456097. Google Scholar
[44]	A. Lunardi, Global solutions of abstract quasilinear parabolic equations,, Journal Differential Equations, 58 (1985), 228. doi: 10.1016/0022-0396(85)90014-2. Google Scholar
[45]	A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", Applied Mathematical Sciences, 44 (1983). doi: 10.1007/978-1-4612-5561-1. Google Scholar
[46]	J. Prüss, Maximal regularity for evolution equations in $L_p$-spaces,, Conf. Semin. Mat. Univ. Bari, (2002), 1. Google Scholar
[47]	J. Prüss and G. Simonett, Maximal regularity for evolution equations in weighted $L_p$-spaces,, Arch. Math., 82 (2004), 415. doi: 10.1007/s00013-004-0585-2. Google Scholar
[48]	J. E. Muñoz Rivera and R. Racke, Smoothing properties, decay, and global existence of solutions to nonlinear coupled systems of thermoelastic type,, SIAM Journal on Mathematical Analysis, 26 (1995), 1547. doi: 10.1137/S0036142993255058. Google Scholar
[49]	J. E. Muñoz Rivera and R. Racke, Large solutions and smoothing properties for nonlinear thermoelastic systems,, Journal of Differential Equations, 127 (1996), 454. doi: 10.1006/jdeq.1996.0078. Google Scholar
[50]	H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators,", North-Holland, (1978). Google Scholar

[1]	P. Gidoni, G. B. Maggiani, R. Scala. Existence and regularity of solutions for an evolution model of perfectly plastic plates. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1783-1826. doi: 10.3934/cpaa.2019084
[2]	Robert Jensen, Andrzej Świech. Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE. Communications on Pure & Applied Analysis, 2005, 4 (1) : 199-207. doi: 10.3934/cpaa.2005.4.187
[3]	T. Tachim Medjo. Existence and uniqueness of strong periodic solutions of the primitive equations of the ocean. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1491-1508. doi: 10.3934/dcds.2010.26.1491
[4]	Salim A. Messaoudi, Abdelfeteh Fareh. Exponential decay for linear damped porous thermoelastic systems with second sound. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 599-612. doi: 10.3934/dcdsb.2015.20.599
[5]	Zhuan Ye. Remark on exponential decay-in-time of global strong solutions to 3D inhomogeneous incompressible micropolar equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6725-6743. doi: 10.3934/dcdsb.2019164
[6]	Maria Grazia Naso. Controllability to trajectories for semilinear thermoelastic plates. Conference Publications, 2005, 2005 (Special) : 672-681. doi: 10.3934/proc.2005.2005.672
[7]	Ramón Quintanilla, Reinhard Racke. Stability for thermoelastic plates with two temperatures. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6333-6352. doi: 10.3934/dcds.2017274
[8]	Yuming Qin, Xinguang Yang, Zhiyong Ma. Global existence of solutions for the thermoelastic Bresse system. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1395-1406. doi: 10.3934/cpaa.2014.13.1395
[9]	Zijuan Wen, Meng Fan, Asim M. Asiri, Ebraheem O. Alzahrani, Mohamed M. El-Dessoky, Yang Kuang. Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 407-420. doi: 10.3934/mbe.2017025
[10]	Vo Anh Khoa, Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence, blow-up and exponential decay of solutions for a porous-elastic system with damping and source terms. Evolution Equations & Control Theory, 2019, 8 (2) : 359-395. doi: 10.3934/eect.2019019
[11]	Barbara Kaltenbacher, Irena Lasiecka. Global existence and exponential decay rates for the Westervelt equation. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 503-523. doi: 10.3934/dcdss.2009.2.503
[12]	Jun Xie, Jinlong Yuan, Dongxia Wang, Weili Liu, Chongyang Liu. Uniqueness of solutions to fuzzy relational equations regarding Max-av composition and strong regularity of the matrices in Max-av algebra. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1007-1022. doi: 10.3934/jimo.2017087
[13]	Pablo Ochoa, Julio Alejo Ruiz. A study of comparison, existence and regularity of viscosity and weak solutions for quasilinear equations in the Heisenberg group. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1091-1115. doi: 10.3934/cpaa.2019053
[14]	Daoyi Xu, Weisong Zhou. Existence-uniqueness and exponential estimate of pathwise solutions of retarded stochastic evolution systems with time smooth diffusion coefficients. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 2161-2180. doi: 10.3934/dcds.2017093
[15]	Stéphane Gerbi, Belkacem Said-Houari. Exponential decay for solutions to semilinear damped wave equation. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 559-566. doi: 10.3934/dcdss.2012.5.559
[16]	Sachiko Ishida, Tomomi Yokota. Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 211-232. doi: 10.3934/dcdss.2020012
[17]	Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2001-2029. doi: 10.3934/cpaa.2013.12.2001
[18]	Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : 349-367. doi: 10.3934/nhm.2016.11.349
[19]	Filippo Dell'Oro, Vittorino Pata. Memory relaxation of type III thermoelastic extensible beams and Berger plates. Evolution Equations & Control Theory, 2012, 1 (2) : 251-270. doi: 10.3934/eect.2012.1.251
[20]	M. Eller, Roberto Triggiani. Exact/approximate controllability of thermoelastic plates with variable thermal coefficients. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 283-302. doi: 10.3934/dcds.2001.7.283

2018 Impact Factor: 1.143

American Institute of Mathematical Sciences

Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors