# American Institute of Mathematical Sciences

February  2016, 36(2): 631-642. doi: 10.3934/dcds.2016.36.631

## Small perturbation of a semilinear pseudo-parabolic equation

 1 School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 2 School of Math. Sci., South China Normal Univ., Guangzhou 510631

Received  May 2014 Revised  February 2015 Published  August 2015

This paper is concerned with large time behavior of solutions for the Cauchy problem of a semilinear pseudo-parabolic equation with small perturbation. It is revealed that small perturbation may develop large variation of solutions with the evolution of time, which is similar to that for the standard heat equation with nonlinear sources.
Citation: Yang Cao, Jingxue Yin. Small perturbation of a semilinear pseudo-parabolic equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 631-642. doi: 10.3934/dcds.2016.36.631
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##### References:
 [1] Juliana Fernandes, Liliane Maia. Blow-up and bounded solutions for a semilinear parabolic problem in a saturable medium. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1297-1318. doi: 10.3934/dcds.2020318 [2] Nguyen Anh Tuan, Donal O'Regan, Dumitru Baleanu, Nguyen H. Tuan. On time fractional pseudo-parabolic equations with nonlocal integral conditions. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020109 [3] Nguyen Huy Tuan, Vo Van Au, Runzhang Xu. Semilinear Caputo time-fractional pseudo-parabolic equations. Communications on Pure & Applied Analysis, 2021, 20 (2) : 583-621. doi: 10.3934/cpaa.2020282 [4] Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388 [5] Tetsuya Ishiwata, Young Chol Yang. Numerical and mathematical analysis of blow-up problems for a stochastic differential equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 909-918. doi: 10.3934/dcdss.2020391 [6] Vo Van Au, Hossein Jafari, Zakia Hammouch, Nguyen Huy Tuan. On a final value problem for a nonlinear fractional pseudo-parabolic equation. Electronic Research Archive, 2021, 29 (1) : 1709-1734. doi: 10.3934/era.2020088 [7] Stanislav Nikolaevich Antontsev, Serik Ersultanovich Aitzhanov, Guzel Rashitkhuzhakyzy Ashurova. An inverse problem for the pseudo-parabolic equation with p-Laplacian. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021005 [8] Manuel del Pino, Monica Musso, Juncheng Wei, Yifu Zhou. Type Ⅱ finite time blow-up for the energy critical heat equation in $\mathbb{R}^4$. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3327-3355. doi: 10.3934/dcds.2020052 [9] Justin Holmer, Chang Liu. Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 215-242. doi: 10.3934/cpaa.2020264 [10] Daniele Bartolucci, Changfeng Gui, Yeyao Hu, Aleks Jevnikar, Wen Yang. Mean field equations on tori: Existence and uniqueness of evenly symmetric blow-up solutions. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3093-3116. doi: 10.3934/dcds.2020039 [11] Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216 [12] Alex H. Ardila, Mykael Cardoso. Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101-119. doi: 10.3934/cpaa.2020259 [13] Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299 [14] Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 [15] Xiaoping Zhai, Yongsheng Li. Global large solutions and optimal time-decay estimates to the Korteweg system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1387-1413. doi: 10.3934/dcds.2020322 [16] Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021003 [17] Olivier Ley, Erwin Topp, Miguel Yangari. Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021007 [18] Yongxiu Shi, Haitao Wan. Refined asymptotic behavior and uniqueness of large solutions to a quasilinear elliptic equation in a borderline case. Electronic Research Archive, , () : -. doi: 10.3934/era.2020119 [19] Jean-Claude Saut, Yuexun Wang. Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1133-1155. doi: 10.3934/dcds.2020312 [20] Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934/cpaa.2020243

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