-
Previous Article
Porous media equations with two weights: Smoothing and decay properties of energy solutions via Poincaré inequalities
- DCDS Home
- This Issue
-
Next Article
Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations
On the moments of solutions to linear parabolic equations involving the biharmonic operator
1. | Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32, Milano, 20133 |
References:
[1] |
71 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 1999. |
[2] |
J. Diff. Eq., 174 (2001), 442-463.
doi: 10.1006/jdeq.2000.3940. |
[3] |
J. Operator Theory, 36 (1996), 179-198. |
[4] |
Adv. Diff. Eq., 13 (2008), 959-976. |
[5] |
J. Math. Anal. Appl., 279 (2003), 710-722.
doi: 10.1016/S0022-247X(03)00062-3. |
[6] |
Nonlin. Anal., 75 (2012), 194-210.
doi: 10.1016/j.na.2011.08.022. |
[7] |
Nonlin. Anal., 75 (2012), 3510-3530.
doi: 10.1016/j.na.2012.01.011. |
[8] |
J. W. Cholewa and A. Rodriguez-Bernal, On the Cahn-Hilliard equation in $H^1(\mathbbR^N)$,, to appear in J. Diff. Eq.., (). Google Scholar |
[9] |
C. R. Acad. Sci. Paris, 330 (2000), 93-98.
doi: 10.1016/S0764-4442(00)00124-5. |
[10] |
C. R. Acad. Sci. Paris, 335 (2002), 805-810.
doi: 10.1016/S1631-073X(02)02567-0. |
[11] |
Adv. Diff. Eq., 9 (2004), 1009-1038. |
[12] |
Izdat. "Nauka", Moscow, (1964). |
[13] |
Disc. Cont. Dynam. Syst., 21 (2008), 1129-1157.
doi: 10.3934/dcds.2008.21.1129. |
[14] |
Nonlin. Diff. Eq. Appl., 5 (2009), 597-655.
doi: 10.1007/s00030-009-0025-x. |
[15] |
Nonlinearity, 18 (2005), 717-746.
doi: 10.1088/0951-7715/18/2/014. |
[16] |
Indiana Univ. Math. J., 51 (2002), 1321-1338.
doi: 10.1512/iumj.2002.51.2131. |
[17] |
Progress in Nonlinear Differential Equations and their Applications 56, Boston (MA) etc.: Birkhäuser, (2004).
doi: 10.1007/978-1-4612-2050-3. |
[18] |
Nonlinearity, 17 (2004), 1075-1099.
doi: 10.1088/0951-7715/17/3/017. |
[19] |
Calc. Var., 30 (2007), 389-415.
doi: 10.1007/s00526-007-0096-7. |
[20] |
Disc. Cont. Dynam. Syst. S., 1 (2008), 83-87. |
[21] |
Nonlinear Analysis, 70 (2009), 2965-2973.
doi: 10.1016/j.na.2008.12.039. |
[22] |
Proc. Roy. Soc. London A., 441 (1993), 423-432.
doi: 10.1098/rspa.1993.0071. |
[23] |
Comm. Partial Differential Equations, 18 (1993), 125-151.
doi: 10.1080/03605309308820923. |
show all references
References:
[1] |
71 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 1999. |
[2] |
J. Diff. Eq., 174 (2001), 442-463.
doi: 10.1006/jdeq.2000.3940. |
[3] |
J. Operator Theory, 36 (1996), 179-198. |
[4] |
Adv. Diff. Eq., 13 (2008), 959-976. |
[5] |
J. Math. Anal. Appl., 279 (2003), 710-722.
doi: 10.1016/S0022-247X(03)00062-3. |
[6] |
Nonlin. Anal., 75 (2012), 194-210.
doi: 10.1016/j.na.2011.08.022. |
[7] |
Nonlin. Anal., 75 (2012), 3510-3530.
doi: 10.1016/j.na.2012.01.011. |
[8] |
J. W. Cholewa and A. Rodriguez-Bernal, On the Cahn-Hilliard equation in $H^1(\mathbbR^N)$,, to appear in J. Diff. Eq.., (). Google Scholar |
[9] |
C. R. Acad. Sci. Paris, 330 (2000), 93-98.
doi: 10.1016/S0764-4442(00)00124-5. |
[10] |
C. R. Acad. Sci. Paris, 335 (2002), 805-810.
doi: 10.1016/S1631-073X(02)02567-0. |
[11] |
Adv. Diff. Eq., 9 (2004), 1009-1038. |
[12] |
Izdat. "Nauka", Moscow, (1964). |
[13] |
Disc. Cont. Dynam. Syst., 21 (2008), 1129-1157.
doi: 10.3934/dcds.2008.21.1129. |
[14] |
Nonlin. Diff. Eq. Appl., 5 (2009), 597-655.
doi: 10.1007/s00030-009-0025-x. |
[15] |
Nonlinearity, 18 (2005), 717-746.
doi: 10.1088/0951-7715/18/2/014. |
[16] |
Indiana Univ. Math. J., 51 (2002), 1321-1338.
doi: 10.1512/iumj.2002.51.2131. |
[17] |
Progress in Nonlinear Differential Equations and their Applications 56, Boston (MA) etc.: Birkhäuser, (2004).
doi: 10.1007/978-1-4612-2050-3. |
[18] |
Nonlinearity, 17 (2004), 1075-1099.
doi: 10.1088/0951-7715/17/3/017. |
[19] |
Calc. Var., 30 (2007), 389-415.
doi: 10.1007/s00526-007-0096-7. |
[20] |
Disc. Cont. Dynam. Syst. S., 1 (2008), 83-87. |
[21] |
Nonlinear Analysis, 70 (2009), 2965-2973.
doi: 10.1016/j.na.2008.12.039. |
[22] |
Proc. Roy. Soc. London A., 441 (1993), 423-432.
doi: 10.1098/rspa.1993.0071. |
[23] |
Comm. Partial Differential Equations, 18 (1993), 125-151.
doi: 10.1080/03605309308820923. |
[1] |
Marcel Braukhoff, Ansgar Jüngel. Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3335-3355. doi: 10.3934/dcdsb.2020234 |
[2] |
Nikolaos Roidos. Expanding solutions of quasilinear parabolic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021026 |
[3] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
[4] |
Yao Nie, Jia Yuan. The Littlewood-Paley $ pth $-order moments in three-dimensional MHD turbulence. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3045-3062. doi: 10.3934/dcds.2020397 |
[5] |
Xiaoming Wang. Quasi-periodic solutions for a class of second order differential equations with a nonlinear damping term. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 543-556. doi: 10.3934/dcdss.2017027 |
[6] |
Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 |
[7] |
Anderson L. A. de Araujo, Marcelo Montenegro. Existence of solution and asymptotic behavior for a class of parabolic equations. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1213-1227. doi: 10.3934/cpaa.2021017 |
[8] |
Bernold Fiedler, Carlos Rocha, Matthias Wolfrum. Sturm global attractors for $S^1$-equivariant parabolic equations. Networks & Heterogeneous Media, 2012, 7 (4) : 617-659. doi: 10.3934/nhm.2012.7.617 |
[9] |
Hongjie Dong, Xinghong Pan. On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021049 |
[10] |
Zhang Chao, Minghua Yang. BMO type space associated with Neumann operator and application to a class of parabolic equations. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021104 |
[11] |
Huan Zhang, Jun Zhou. Asymptotic behaviors of solutions to a sixth-order Boussinesq equation with logarithmic nonlinearity. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021034 |
[12] |
Weisong Dong, Chang Li. Second order estimates for complex Hessian equations on Hermitian manifolds. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2619-2633. doi: 10.3934/dcds.2020377 |
[13] |
Dariusz Idczak. A Gronwall lemma for functions of two variables and its application to partial differential equations of fractional order. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021019 |
[14] |
Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 |
[15] |
Yimin Zhang, Youjun Wang, Yaotian Shen. Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1037-1054. doi: 10.3934/cpaa.2011.10.1037 |
[16] |
Arunima Bhattacharya, Micah Warren. $ C^{2, \alpha} $ estimates for solutions to almost Linear elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021024 |
[17] |
Yahui Niu. A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021027 |
[18] |
Pengyu Chen. Periodic solutions to non-autonomous evolution equations with multi-delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2921-2939. doi: 10.3934/dcdsb.2020211 |
[19] |
Lidan Wang, Lihe Wang, Chunqin Zhou. Classification of positive solutions for fully nonlinear elliptic equations in unbounded cylinders. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1241-1261. doi: 10.3934/cpaa.2021019 |
[20] |
Tomasz Kosmala, Markus Riedle. Variational solutions of stochastic partial differential equations with cylindrical Lévy noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2879-2898. doi: 10.3934/dcdsb.2020209 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]