-
Previous Article
On the Ornstein Uhlenbeck operator perturbed by singular potentials in $L^p$--spaces
- DCDS Home
- This Issue
-
Next Article
Resolution and optimal regularity for a biharmonic equation with impedance boundary conditions and some generalizations
Local Hadamard well--posedness and blow--up for reaction--diffusion equations with non--linear dynamical boundary conditions
1. | Dipartimento di Matematica "F. Enriques", Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy |
2. | Dipartimento di Matematica ed Informatica, Università di Perugia, Via Vanvitelli, 1, 06123 Perugia, Italy |
References:
[1] |
Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975, Pure and Applied Mathematics, 65, 1975. |
[2] |
J. Differential Equations, 72 (1988), 201-269.
doi: 10.1016/0022-0396(88)90156-8. |
[3] |
C. R. Acad. Sci. Paris, 256 (1963), 5042-5044. |
[4] |
Nonlinear Anal., 73 (2010), 1952-1965.
doi: 10.1016/j.na.2010.05.024. |
[5] |
Commun. Pure Appl. Anal., 9 (2010), 1161-1188.
doi: 10.3934/cpaa.2010.9.1161. |
[6] |
Arch. Ration. Mech. Anal., 196 (2010), 489-516.
doi: 10.1007/s00205-009-0241-x. |
[7] |
I. Bejenaru, J. I. Díaz and I. I. Vrabie, An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions,, Electron. J. Differential Equations, 2001 ().
|
[8] |
Discrete Contin. Dyn. Syst., 22 (2008), 835-860.
doi: 10.3934/dcds.2008.22.835. |
[9] |
J. Differential Equations, 249 (2010), 654-683.
doi: 10.1016/j.jde.2010.03.009. |
[10] |
Universitext, Springer, New York, 2011. |
[11] |
H. Brezis and T. Cazenave, Unpublished, Book., (). Google Scholar |
[12] |
Adv. Differential Equations, 1 (1996), 73-90. |
[13] |
J. Differential Equations, 236 (2007), 407-459.
doi: 10.1016/j.jde.2007.02.004. |
[14] |
J. Differential Equations, 203 (2004), 119-158.
doi: 10.1016/j.jde.2004.04.011. |
[15] |
Comm. Partial Differential Equations, 27 (2002), 1901-1951.
doi: 10.1081/PDE-120016132. |
[16] |
McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. |
[17] |
Japan J. Indust. Appl. Math., 9 (1992), 181-203.
doi: 10.1007/BF03167565. |
[18] |
Comput. Math. Appl., 60 (2010), 670-679.
doi: 10.1016/j.camwa.2010.05.015. |
[19] |
Math. Ann., 284 (1989), 285-305.
doi: 10.1007/BF01442877. |
[20] |
Comm. Partial Differential Equations, 18 (1993), 1309-1364.
doi: 10.1080/03605309308820976. |
[21] |
Differential Integral Equations, 8 (1995), 247-267. |
[22] |
Nonlinear Anal., 68 (2008), 1723-1732.
doi: 10.1016/j.na.2007.01.005. |
[23] |
Discrete Contin. Dyn. Syst., 8 (2002), 399-433, Current Developments in Partial Differential Equations (Temuco, 1999).
doi: 10.3934/dcds.2002.8.399. |
[24] |
J. Differential Equations, 109 (1994), 295-308.
doi: 10.1006/jdeq.1994.1051. |
[25] |
Adv. Differential Equations, 13 (2008), 1051-1074. |
[26] |
J. Math. Anal. Appl., 333 (2007), 839-862.
doi: 10.1016/j.jmaa.2006.11.050. |
[27] |
Proc. Roy. Soc. Edinburgh Sect. A, 105 (1987), 101-115.
doi: 10.1017/S0308210500021946. |
[28] |
Proc. Roy. Soc. Edinburgh Sect. A, 113 (1989), 43-60.
doi: 10.1017/S0308210500023945. |
[29] |
J. Differential Equations, 212 (2005), 114-128.
doi: 10.1016/j.jde.2004.10.021. |
[30] |
Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 215-218.
doi: 10.1016/j.anihpc.2006.12.002. |
[31] |
Hokkaido Math. J., 21 (1992), 221-229. |
[32] |
J. Differential Equations, 75 (1988), 53-87.
doi: 10.1016/0022-0396(88)90129-5. |
[33] |
Arch. Rational Mech. Anal., 51 (1973), 371-386. |
[34] |
SIAM Rev., 32 (1990), 262-288.
doi: 10.1137/1032046. |
[35] |
J. Differential Equations, 142 (1998), 212-229.
doi: 10.1006/jdeq.1997.3362. |
[36] |
J. Differential Equations, 16 (1974), 319-334.
doi: 10.1016/0022-0396(74)90018-7. |
[37] |
Proc. Amer. Math. Soc. 46 (1974), 277-284. |
[38] |
Arch. Rational Mech. Anal., 137 (1997), 341-361.
doi: 10.1007/s002050050032. |
[39] |
Math. Methods Appl. Sci., 9 (1987), 127-136.
doi: 10.1002/mma.1670090111. |
[40] |
J. Reine Angew. Math., 374 (1987), 1-23. |
[41] |
Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968. |
[42] |
Bull. Soc. Math. France, 93 (1965), 43-96. |
[43] |
Progress in Nonlinear Differential Equations and Their Applications, 16, Birkhäuser Verlag, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[44] |
Nonlinear Anal., 50 (2002), Ser. A: Theory Methods, 223-250.
doi: 10.1016/S0362-546X(01)00748-9. |
[45] |
Arch. Rational Mech. Anal., 45 (1972), 294-320. |
[46] |
J. Differential Equations, 193 (2003), 212-238.
doi: 10.1016/S0022-0396(03)00128-1. |
[47] |
Appl. Anal., 87 (2008), 699-707.
doi: 10.1080/00036810802189662. |
[48] |
Int. J. Pure Appl. Math., 48 (2008), 193-202. |
[49] |
J. Math. Anal. Appl., 354 (2009), 394-396.
doi: 10.1016/j.jmaa.2009.01.010. |
[50] |
J. Differential Equations, 150 (1998), 203-214.
doi: 10.1006/jdeq.1998.3477. |
[51] |
Discrete Contin. Dyn. Syst., 18 (2007), 15-38.
doi: 10.3934/dcds.2007.18.15. |
[52] |
Differential Integral Equations, 16 (2003), 13-50. |
[53] |
Ann. Mat. Pura Appl. (4), 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[54] |
Pacific J. Math., 19 (1966), 543-551.
doi: 10.2140/pjm.1966.19.543. |
[55] |
Applied Mathematical Sciences, 117, Springer-Verlag, New York, 1997, Nonlinear Equations, Corrected Reprint of the 1996 Original. |
[56] |
Soviet Math. Dokl., 1 (1960), 132-133. |
[57] |
Arch. Rational Mech. Anal., 149 (1999), 155-182.
doi: 10.1007/s002050050171. |
[58] |
Rend. Istit. Mat. Univ. Trieste, 31 (2000), 245-275, Workshop on Blow-up and Global Existence of Solutions for Parabolic and Hyperbolic Problems (Trieste, 1999). |
[59] |
J. Differential Equations, 186 (2002), 259-298.
doi: 10.1016/S0022-0396(02)00023-2. |
[60] |
Glasg. Math. J., 44 (2002), 375-395.
doi: 10.1017/S0017089502030045. |
[61] |
Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), 1-33.
doi: 10.1017/S0308210500003838. |
[62] |
Proc. London Math. Soc. (3), 93 (2006), 418-446.
doi: 10.1112/S0024611506015875. |
[63] |
Comm. Partial Differential Equations, 28 (2003), 223-247.
doi: 10.1081/PDE-120019380. |
[64] |
Discrete Contin. Dyn. Syst., 2007, Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference, suppl., 1031-1041. |
[65] |
Graduate Texts in Mathematics, 120, Springer-Verlag, New York, 1989, Sobolev spaces and functions of bounded variation.
doi: 10.1007/978-1-4612-1015-3. |
show all references
References:
[1] |
Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975, Pure and Applied Mathematics, 65, 1975. |
[2] |
J. Differential Equations, 72 (1988), 201-269.
doi: 10.1016/0022-0396(88)90156-8. |
[3] |
C. R. Acad. Sci. Paris, 256 (1963), 5042-5044. |
[4] |
Nonlinear Anal., 73 (2010), 1952-1965.
doi: 10.1016/j.na.2010.05.024. |
[5] |
Commun. Pure Appl. Anal., 9 (2010), 1161-1188.
doi: 10.3934/cpaa.2010.9.1161. |
[6] |
Arch. Ration. Mech. Anal., 196 (2010), 489-516.
doi: 10.1007/s00205-009-0241-x. |
[7] |
I. Bejenaru, J. I. Díaz and I. I. Vrabie, An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions,, Electron. J. Differential Equations, 2001 ().
|
[8] |
Discrete Contin. Dyn. Syst., 22 (2008), 835-860.
doi: 10.3934/dcds.2008.22.835. |
[9] |
J. Differential Equations, 249 (2010), 654-683.
doi: 10.1016/j.jde.2010.03.009. |
[10] |
Universitext, Springer, New York, 2011. |
[11] |
H. Brezis and T. Cazenave, Unpublished, Book., (). Google Scholar |
[12] |
Adv. Differential Equations, 1 (1996), 73-90. |
[13] |
J. Differential Equations, 236 (2007), 407-459.
doi: 10.1016/j.jde.2007.02.004. |
[14] |
J. Differential Equations, 203 (2004), 119-158.
doi: 10.1016/j.jde.2004.04.011. |
[15] |
Comm. Partial Differential Equations, 27 (2002), 1901-1951.
doi: 10.1081/PDE-120016132. |
[16] |
McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. |
[17] |
Japan J. Indust. Appl. Math., 9 (1992), 181-203.
doi: 10.1007/BF03167565. |
[18] |
Comput. Math. Appl., 60 (2010), 670-679.
doi: 10.1016/j.camwa.2010.05.015. |
[19] |
Math. Ann., 284 (1989), 285-305.
doi: 10.1007/BF01442877. |
[20] |
Comm. Partial Differential Equations, 18 (1993), 1309-1364.
doi: 10.1080/03605309308820976. |
[21] |
Differential Integral Equations, 8 (1995), 247-267. |
[22] |
Nonlinear Anal., 68 (2008), 1723-1732.
doi: 10.1016/j.na.2007.01.005. |
[23] |
Discrete Contin. Dyn. Syst., 8 (2002), 399-433, Current Developments in Partial Differential Equations (Temuco, 1999).
doi: 10.3934/dcds.2002.8.399. |
[24] |
J. Differential Equations, 109 (1994), 295-308.
doi: 10.1006/jdeq.1994.1051. |
[25] |
Adv. Differential Equations, 13 (2008), 1051-1074. |
[26] |
J. Math. Anal. Appl., 333 (2007), 839-862.
doi: 10.1016/j.jmaa.2006.11.050. |
[27] |
Proc. Roy. Soc. Edinburgh Sect. A, 105 (1987), 101-115.
doi: 10.1017/S0308210500021946. |
[28] |
Proc. Roy. Soc. Edinburgh Sect. A, 113 (1989), 43-60.
doi: 10.1017/S0308210500023945. |
[29] |
J. Differential Equations, 212 (2005), 114-128.
doi: 10.1016/j.jde.2004.10.021. |
[30] |
Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 215-218.
doi: 10.1016/j.anihpc.2006.12.002. |
[31] |
Hokkaido Math. J., 21 (1992), 221-229. |
[32] |
J. Differential Equations, 75 (1988), 53-87.
doi: 10.1016/0022-0396(88)90129-5. |
[33] |
Arch. Rational Mech. Anal., 51 (1973), 371-386. |
[34] |
SIAM Rev., 32 (1990), 262-288.
doi: 10.1137/1032046. |
[35] |
J. Differential Equations, 142 (1998), 212-229.
doi: 10.1006/jdeq.1997.3362. |
[36] |
J. Differential Equations, 16 (1974), 319-334.
doi: 10.1016/0022-0396(74)90018-7. |
[37] |
Proc. Amer. Math. Soc. 46 (1974), 277-284. |
[38] |
Arch. Rational Mech. Anal., 137 (1997), 341-361.
doi: 10.1007/s002050050032. |
[39] |
Math. Methods Appl. Sci., 9 (1987), 127-136.
doi: 10.1002/mma.1670090111. |
[40] |
J. Reine Angew. Math., 374 (1987), 1-23. |
[41] |
Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968. |
[42] |
Bull. Soc. Math. France, 93 (1965), 43-96. |
[43] |
Progress in Nonlinear Differential Equations and Their Applications, 16, Birkhäuser Verlag, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[44] |
Nonlinear Anal., 50 (2002), Ser. A: Theory Methods, 223-250.
doi: 10.1016/S0362-546X(01)00748-9. |
[45] |
Arch. Rational Mech. Anal., 45 (1972), 294-320. |
[46] |
J. Differential Equations, 193 (2003), 212-238.
doi: 10.1016/S0022-0396(03)00128-1. |
[47] |
Appl. Anal., 87 (2008), 699-707.
doi: 10.1080/00036810802189662. |
[48] |
Int. J. Pure Appl. Math., 48 (2008), 193-202. |
[49] |
J. Math. Anal. Appl., 354 (2009), 394-396.
doi: 10.1016/j.jmaa.2009.01.010. |
[50] |
J. Differential Equations, 150 (1998), 203-214.
doi: 10.1006/jdeq.1998.3477. |
[51] |
Discrete Contin. Dyn. Syst., 18 (2007), 15-38.
doi: 10.3934/dcds.2007.18.15. |
[52] |
Differential Integral Equations, 16 (2003), 13-50. |
[53] |
Ann. Mat. Pura Appl. (4), 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[54] |
Pacific J. Math., 19 (1966), 543-551.
doi: 10.2140/pjm.1966.19.543. |
[55] |
Applied Mathematical Sciences, 117, Springer-Verlag, New York, 1997, Nonlinear Equations, Corrected Reprint of the 1996 Original. |
[56] |
Soviet Math. Dokl., 1 (1960), 132-133. |
[57] |
Arch. Rational Mech. Anal., 149 (1999), 155-182.
doi: 10.1007/s002050050171. |
[58] |
Rend. Istit. Mat. Univ. Trieste, 31 (2000), 245-275, Workshop on Blow-up and Global Existence of Solutions for Parabolic and Hyperbolic Problems (Trieste, 1999). |
[59] |
J. Differential Equations, 186 (2002), 259-298.
doi: 10.1016/S0022-0396(02)00023-2. |
[60] |
Glasg. Math. J., 44 (2002), 375-395.
doi: 10.1017/S0017089502030045. |
[61] |
Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), 1-33.
doi: 10.1017/S0308210500003838. |
[62] |
Proc. London Math. Soc. (3), 93 (2006), 418-446.
doi: 10.1112/S0024611506015875. |
[63] |
Comm. Partial Differential Equations, 28 (2003), 223-247.
doi: 10.1081/PDE-120019380. |
[64] |
Discrete Contin. Dyn. Syst., 2007, Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference, suppl., 1031-1041. |
[65] |
Graduate Texts in Mathematics, 120, Springer-Verlag, New York, 1989, Sobolev spaces and functions of bounded variation.
doi: 10.1007/978-1-4612-1015-3. |
[1] |
Jihoon Lee, Nguyen Thanh Nguyen. Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1263-1296. doi: 10.3934/cpaa.2021020 |
[2] |
Bouthaina Abdelhedi, Hatem Zaag. Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021032 |
[3] |
Asato Mukai, Yukihiro Seki. Refined construction of type II blow-up solutions for semilinear heat equations with Joseph–Lundgren supercritical nonlinearity. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021060 |
[4] |
Vandana Sharma. Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions. Communications on Pure & Applied Analysis, 2021, 20 (3) : 955-974. doi: 10.3934/cpaa.2021001 |
[5] |
Yingdan Ji, Wen Tan. Global well-posedness of a 3D Stokes-Magneto equations with fractional magnetic diffusion. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3271-3278. doi: 10.3934/dcdsb.2020227 |
[6] |
Tadahiro Oh, Yuzhao Wang. On global well-posedness of the modified KdV equation in modulation spaces. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2971-2992. doi: 10.3934/dcds.2020393 |
[7] |
Guangying Lv, Jinlong Wei, Guang-an Zou. Noise and stability in reaction-diffusion equations. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021005 |
[8] |
Xavier Carvajal, Liliana Esquivel, Raphael Santos. On local well-posedness and ill-posedness results for a coupled system of mkdv type equations. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2699-2723. doi: 10.3934/dcds.2020382 |
[9] |
Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223 |
[10] |
Masahiro Ikeda, Ziheng Tu, Kyouhei Wakasa. Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021011 |
[11] |
Thomas Y. Hou, Ruo Li. Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 637-642. doi: 10.3934/dcds.2007.18.637 |
[12] |
Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 |
[13] |
Pengyan Ding, Zhijian Yang. Well-posedness and attractor for a strongly damped wave equation with supercritical nonlinearity on $ \mathbb{R}^{N} $. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1059-1076. doi: 10.3934/cpaa.2021006 |
[14] |
Mario Bukal. Well-posedness and convergence of a numerical scheme for the corrected Derrida-Lebowitz-Speer-Spohn equation using the Hellinger distance. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3389-3414. doi: 10.3934/dcds.2021001 |
[15] |
Andreia Chapouto. A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3915-3950. doi: 10.3934/dcds.2021022 |
[16] |
Mohamed Ouzahra. Approximate controllability of the semilinear reaction-diffusion equation governed by a multiplicative control. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021081 |
[17] |
Meng-Xue Chang, Bang-Sheng Han, Xiao-Ming Fan. Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect. Electronic Research Archive, , () : -. doi: 10.3934/era.2021024 |
[18] |
Bo Duan, Zhengce Zhang. A reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021067 |
[19] |
Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3063-3092. doi: 10.3934/dcds.2020398 |
[20] |
Nabahats Dib-Baghdadli, Rabah Labbas, Tewfik Mahdjoub, Ahmed Medeghri. On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021004 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]