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Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth
Gradient blowup rate for a semilinear parabolic equation
1. | College of Science, Xi’an Jiaotong University, Xi’an, 710049, China |
2. | Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 |
[1] |
Jong-Shenq Guo, Bei Hu. Blowup rate estimates for the heat equation with a nonlinear gradient source term. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 927-937. doi: 10.3934/dcds.2008.20.927 |
[2] |
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 |
[3] |
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 |
[4] |
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 |
[5] |
Xuan Liu, Ting Zhang. $ H^2 $ blowup result for a Schrödinger equation with nonlinear source term. Electronic Research Archive, 2020, 28 (2) : 777-794. doi: 10.3934/era.2020039 |
[6] |
Thierry Cazenave, Yvan Martel, Lifeng Zhao. Finite-time blowup for a Schrödinger equation with nonlinear source term. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1171-1183. doi: 10.3934/dcds.2019050 |
[7] |
Jong-Shenq Guo, Satoshi Sasayama, Chi-Jen Wang. Blowup rate estimate for a system of semilinear parabolic equations. Communications on Pure and Applied Analysis, 2009, 8 (2) : 711-718. doi: 10.3934/cpaa.2009.8.711 |
[8] |
Chunlai Mu, Zhaoyin Xiang. Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux. Communications on Pure and Applied Analysis, 2007, 6 (2) : 487-503. doi: 10.3934/cpaa.2007.6.487 |
[9] |
Masahoto Ohta, Grozdena Todorova. Remarks on global existence and blowup for damped nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2009, 23 (4) : 1313-1325. doi: 10.3934/dcds.2009.23.1313 |
[10] |
Zaihui Gan, Boling Guo, Jian Zhang. Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1303-1312. doi: 10.3934/cpaa.2009.8.1303 |
[11] |
Lawrence Ein, Wenbo Niu, Jinhyung Park. On blowup of secant varieties of curves. Electronic Research Archive, 2021, 29 (6) : 3649-3654. doi: 10.3934/era.2021055 |
[12] |
Bertram Düring, Daniel Matthes, Josipa Pina Milišić. A gradient flow scheme for nonlinear fourth order equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 935-959. doi: 10.3934/dcdsb.2010.14.935 |
[13] |
Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma, Dijana Mosić. A survey of gradient methods for solving nonlinear optimization. Electronic Research Archive, 2020, 28 (4) : 1573-1624. doi: 10.3934/era.2020115 |
[14] |
Liangjun Weng. The interior gradient estimate for some nonlinear curvature equations. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1601-1612. doi: 10.3934/cpaa.2019076 |
[15] |
Xiaohong Li, Fengquan Li. Nonexistence of solutions for nonlinear differential inequalities with gradient nonlinearities. Communications on Pure and Applied Analysis, 2012, 11 (3) : 935-943. doi: 10.3934/cpaa.2012.11.935 |
[16] |
Yanghong Huang, Andrea Bertozzi. Asymptotics of blowup solutions for the aggregation equation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1309-1331. doi: 10.3934/dcdsb.2012.17.1309 |
[17] |
Congming Peng, Dun Zhao. Global existence and blowup on the energy space for the inhomogeneous fractional nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3335-3356. doi: 10.3934/dcdsb.2018323 |
[18] |
Paolo Baiti, Helge Kristian Jenssen. Blowup in $\mathbf{L^{\infty}}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 837-853. doi: 10.3934/dcds.2001.7.837 |
[19] |
Ping Lin. Feedback controllability for blowup points of semilinear heat equations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1425-1434. doi: 10.3934/dcdsb.2017068 |
[20] |
Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz. Morrey spaces norms and criteria for blowup in chemotaxis models. Networks and Heterogeneous Media, 2016, 11 (2) : 239-250. doi: 10.3934/nhm.2016.11.239 |
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