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On the time evolution of Wigner measures for Schrödinger equations
Boundedness and blowup solutions for quasilinear parabolic systems with lower order terms
1. | Department of Mathematics, Physics & Geology, Cape Breton University, Sydney, NS, Canada, B1P 6L2 |
[1] |
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 |
[2] |
Siegfried Carl, Christoph Tietz. Quasilinear elliptic equations with measures and multi-valued lower order terms. Discrete and Continuous Dynamical Systems - S, 2018, 11 (2) : 193-212. doi: 10.3934/dcdss.2018012 |
[3] |
Angelo Favini, Alfredo Lorenzi, Hiroki Tanabe, Atsushi Yagi. An $L^p$-approach to singular linear parabolic equations with lower order terms. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 989-1008. doi: 10.3934/dcds.2008.22.989 |
[4] |
Luisa Malaguti, Cristina Marcelli. Existence of bounded trajectories via upper and lower solutions. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 575-590. doi: 10.3934/dcds.2000.6.575 |
[5] |
Chi-Cheung Poon. Blowup rate of solutions of a degenerate nonlinear parabolic equation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5317-5336. doi: 10.3934/dcdsb.2019060 |
[6] |
Roberta Filippucci, Chiara Lini. Existence of solutions for quasilinear Dirichlet problems with gradient terms. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 267-286. doi: 10.3934/dcdss.2019019 |
[7] |
Anne Mund, Christina Kuttler, Judith Pérez-Velázquez. Existence and uniqueness of solutions to a family of semi-linear parabolic systems using coupled upper-lower solutions. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5695-5707. doi: 10.3934/dcdsb.2019102 |
[8] |
Nikolaos Roidos. Expanding solutions of quasilinear parabolic equations. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1413-1429. doi: 10.3934/cpaa.2021026 |
[9] |
Bingbing Ding, Ingo Witt, Huicheng Yin. Blowup time and blowup mechanism of small data solutions to general 2-D quasilinear wave equations. Communications on Pure and Applied Analysis, 2017, 16 (3) : 719-744. doi: 10.3934/cpaa.2017035 |
[10] |
Denis R. Akhmetov, Renato Spigler. $L^1$-estimates for the higher-order derivatives of solutions to parabolic equations subject to initial values of bounded total variation. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1051-1074. doi: 10.3934/cpaa.2007.6.1051 |
[11] |
Zhengce Zhang, Yanyan Li. Gradient blowup solutions of a semilinear parabolic equation with exponential source. Communications on Pure and Applied Analysis, 2013, 12 (1) : 269-280. doi: 10.3934/cpaa.2013.12.269 |
[12] |
Zhengce Zhang, Yan Li. Global existence and gradient blowup of solutions for a semilinear parabolic equation with exponential source. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 3019-3029. doi: 10.3934/dcdsb.2014.19.3019 |
[13] |
Maria Assunta Pozio, Alberto Tesei. On the uniqueness of bounded solutions to singular parabolic problems. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 117-137. doi: 10.3934/dcds.2005.13.117 |
[14] |
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 |
[15] |
Elena-Alexandra Melnig. Internal feedback stabilization for parabolic systems coupled in zero or first order terms. Evolution Equations and Control Theory, 2021, 10 (2) : 333-351. doi: 10.3934/eect.2020069 |
[16] |
Jean Mawhin. Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1065-1076. doi: 10.3934/dcdss.2013.6.1065 |
[17] |
Shaohua Chen, Runzhang Xu, Hongtao Yang. Global and blowup solutions for general Lotka-Volterra systems. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1757-1768. doi: 10.3934/cpaa.2016012 |
[18] |
Grzegorz Karch, Kanako Suzuki, Jacek Zienkiewicz. Finite-time blowup of solutions to some activator-inhibitor systems. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4997-5010. doi: 10.3934/dcds.2016016 |
[19] |
Huiling Li, Mingxin Wang. Properties of blow-up solutions to a parabolic system with nonlinear localized terms. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 683-700. doi: 10.3934/dcds.2005.13.683 |
[20] |
Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810 |
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