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Global well-posedness of the viscous Boussinesq equations
On uniqueness of positive entire solutions and other properties of linear parabolic equations
1. | School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States |
[1] |
J. Húska, Peter Poláčik, M.V. Safonov. Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Conference Publications, 2005, 2005 (Special) : 427-435. doi: 10.3934/proc.2005.2005.427 |
[2] |
J. Húska, Peter Poláčik. Exponential separation and principal Floquet bundles for linear parabolic equations on $R^N$. Discrete and Continuous Dynamical Systems, 2008, 20 (1) : 81-113. doi: 10.3934/dcds.2008.20.81 |
[3] |
Soohyun Bae, Yūki Naito. Separation structure of radial solutions for semilinear elliptic equations with exponential nonlinearity. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4537-4554. doi: 10.3934/dcds.2018198 |
[4] |
Monica Motta, Caterina Sartori. Uniqueness of solutions for second order Bellman-Isaacs equations with mixed boundary conditions. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 739-765. doi: 10.3934/dcds.2008.20.739 |
[5] |
Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 763-800. doi: 10.3934/dcds.2008.21.763 |
[6] |
Alberto Farina. Some symmetry results for entire solutions of an elliptic system arising in phase separation. Discrete and Continuous Dynamical Systems, 2014, 34 (6) : 2505-2511. doi: 10.3934/dcds.2014.34.2505 |
[7] |
N. V. Krylov. Uniqueness for Lp-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2495-2516. doi: 10.3934/cpaa.2018119 |
[8] |
Lucas Bonifacius, Ira Neitzel. Second order optimality conditions for optimal control of quasilinear parabolic equations. Mathematical Control and Related Fields, 2018, 8 (1) : 1-34. doi: 10.3934/mcrf.2018001 |
[9] |
Walter Allegretto, Liqun Cao, Yanping Lin. Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 543-576. doi: 10.3934/dcds.2008.20.543 |
[10] |
Alberto Boscaggin, Fabio Zanolin. Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 89-110. doi: 10.3934/dcds.2013.33.89 |
[11] |
Hiroshi Watanabe. Existence and uniqueness of entropy solutions to strongly degenerate parabolic equations with discontinuous coefficients. Conference Publications, 2013, 2013 (special) : 781-790. doi: 10.3934/proc.2013.2013.781 |
[12] |
Peiying Chen. Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations. Electronic Research Announcements, 2017, 24: 38-52. doi: 10.3934/era.2017.24.005 |
[13] |
Kenneth Hvistendahl Karlsen, Nils Henrik Risebro. On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1081-1104. doi: 10.3934/dcds.2003.9.1081 |
[14] |
Seick Kim, Longjuan Xu. Green's function for second order parabolic equations with singular lower order coefficients. Communications on Pure and Applied Analysis, 2022, 21 (1) : 1-21. doi: 10.3934/cpaa.2021164 |
[15] |
Ahmed Y. Abdallah. Exponential attractors for second order lattice dynamical systems. Communications on Pure and Applied Analysis, 2009, 8 (3) : 803-813. doi: 10.3934/cpaa.2009.8.803 |
[16] |
Xuelei Wang, Dingbian Qian, Xiying Sun. Periodic solutions of second order equations with asymptotical non-resonance. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4715-4726. doi: 10.3934/dcds.2018207 |
[17] |
Yuan Guo, Xiaofei Gao, Desheng Li. Structure of the set of bounded solutions for a class of nonautonomous second order differential equations. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1607-1616. doi: 10.3934/cpaa.2010.9.1607 |
[18] |
John R. Graef, Lingju Kong, Min Wang. Existence of homoclinic solutions for second order difference equations with $p$-laplacian. Conference Publications, 2015, 2015 (special) : 533-539. doi: 10.3934/proc.2015.0533 |
[19] |
Zhiming Guo, Xiaomin Zhang. Multiplicity results for periodic solutions to a class of second order delay differential equations. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1529-1542. doi: 10.3934/cpaa.2010.9.1529 |
[20] |
Claudia Anedda, Giovanni Porru. Second order estimates for boundary blow-up solutions of elliptic equations. Conference Publications, 2007, 2007 (Special) : 54-63. doi: 10.3934/proc.2007.2007.54 |
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