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On the Cauchy problem for differential-difference parabolic equations with high-order nonlocal terms of general kind
Universal bounds for quasilinear parabolic equations with convection
1. | Department of Mathematics, Faculty of Engineering, Kokushikan University, 4-28-1 Setagaya Setagaya-ku Tokyo, 154-8515, Japan |
[1] |
Jong-Shenq Guo. Blow-up behavior for a quasilinear parabolic equation with nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 71-84. doi: 10.3934/dcds.2007.18.71 |
[2] |
Zhiqing Liu, Zhong Bo Fang. Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3619-3635. doi: 10.3934/dcdsb.2016113 |
[3] |
Pavol Quittner, Philippe Souplet. Blow-up rate of solutions of parabolic poblems with nonlinear boundary conditions. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 671-681. doi: 10.3934/dcdss.2012.5.671 |
[4] |
Yoshikazu Giga. Interior derivative blow-up for quasilinear parabolic equations. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 449-461. doi: 10.3934/dcds.1995.1.449 |
[5] |
Yohei Fujishima. Blow-up set for a superlinear heat equation and pointedness of the initial data. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4617-4645. doi: 10.3934/dcds.2014.34.4617 |
[6] |
Sachiko Ishida, Tomomi Yokota. Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2569-2596. doi: 10.3934/dcdsb.2013.18.2569 |
[7] |
Steven D. Taliaferro. Initial Pointwise Bounds and Blow-up for Parabolic Choquard-Pekar Inequalities. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5211-5252. doi: 10.3934/dcds.2017226 |
[8] |
C. Brändle, F. Quirós, Julio D. Rossi. Non-simultaneous blow-up for a quasilinear parabolic system with reaction at the boundary. Communications on Pure and Applied Analysis, 2005, 4 (3) : 523-536. doi: 10.3934/cpaa.2005.4.523 |
[9] |
Johannes Lankeit. Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 233-255. doi: 10.3934/dcdss.2020013 |
[10] |
Juntang Ding, Chenyu Dong. Blow-up results of the positive solution for a weakly coupled quasilinear parabolic system. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021222 |
[11] |
Yuya Tanaka, Tomomi Yokota. Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022075 |
[12] |
Yohei Fujishima. On the effect of higher order derivatives of initial data on the blow-up set for a semilinear heat equation. Communications on Pure and Applied Analysis, 2018, 17 (2) : 449-475. doi: 10.3934/cpaa.2018025 |
[13] |
Jian Zhang, Shihui Zhu, Xiaoguang Li. Rate of $L^2$-concentration of the blow-up solution for critical nonlinear Schrödinger equation with potential. Mathematical Control and Related Fields, 2011, 1 (1) : 119-127. doi: 10.3934/mcrf.2011.1.119 |
[14] |
Victor A. Galaktionov, Juan-Luis Vázquez. The problem Of blow-up in nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 399-433. doi: 10.3934/dcds.2002.8.399 |
[15] |
Pablo Álvarez-Caudevilla, Jonathan D. Evans, Victor A. Galaktionov. Gradient blow-up for a fourth-order quasilinear Boussinesq-type equation. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3913-3938. doi: 10.3934/dcds.2018170 |
[16] |
Miaoqing Tian, Sining Zheng. Global boundedness versus finite-time blow-up of solutions to a quasilinear fully parabolic Keller-Segel system of two species. Communications on Pure and Applied Analysis, 2016, 15 (1) : 243-260. doi: 10.3934/cpaa.2016.15.243 |
[17] |
Ronghua Jiang, Jun Zhou. Blow-up and global existence of solutions to a parabolic equation associated with the fraction p-Laplacian. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1205-1226. doi: 10.3934/cpaa.2019058 |
[18] |
Xiaoliang Li, Baiyu Liu. Finite time blow-up and global solutions for a nonlocal parabolic equation with Hartree type nonlinearity. Communications on Pure and Applied Analysis, 2020, 19 (6) : 3093-3112. doi: 10.3934/cpaa.2020134 |
[19] |
Shota Sato. Blow-up at space infinity of a solution with a moving singularity for a semilinear parabolic equation. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1225-1237. doi: 10.3934/cpaa.2011.10.1225 |
[20] |
Alberto Bressan, Massimo Fonte. On the blow-up for a discrete Boltzmann equation in the plane. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 1-12. doi: 10.3934/dcds.2005.13.1 |
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