Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions

L. E. Payne; G. A. Philippin

doi:10.1017/S0308210511000485

Abstract

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This paper deals with the blow-up of solutions to a class of parabolic problems with time-dependent coefficients under homogeneous Neumann boundary conditions. For one set of problems in this class we show that no global solution can exist. For another we derive lower bounds for the time of blow-up when blow-up occurs.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Marras, Monica and Vernier Piro, Stella 2014. Reaction-diffusion problems under non-local boundary conditions with blow-up solutions. Journal of Inequalities and Applications, Vol. 2014, Issue. 1,

Fang, Zhong Bo and Wang, Yuxiang 2015. Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Zeitschrift für angewandte Mathematik und Physik, Vol. 66, Issue. 5, p. 2525.

Öztürk, E. and Kallı, K. 2016. Existence and Nonexistence of Solutions of the Reaction-Diffusion Equation with Robin Boundary Condition. Ukrainian Mathematical Journal, Vol. 68, Issue. 3, p. 475.

Liu, Zhiqing and Fang, Zhong Bo 2016. Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Discrete and Continuous Dynamical Systems - Series B, Vol. 21, Issue. 10, p. 3619.

Ding, Juntang and Hu, Hongjuan 2017. Blow-up solutions for nonlinear reaction diffusion equations under Neumann boundary conditions. Applicable Analysis, Vol. 96, Issue. 4, p. 549.

Ding, Juntang 2017. Blow-up phenomena for p-Laplacian parabolic problems with Neumann boundary conditions. Boundary Value Problems, Vol. 2017, Issue. 1,

Tao, Xueyan and Fang, Zhong Bo 2017. Blow-up phenomena for a nonlinear reaction–diffusion system with time dependent coefficients. Computers & Mathematics with Applications, Vol. 74, Issue. 10, p. 2520.

Tang, Gusheng 2017. Blow-up phenomena for a parabolic system with gradient nonlinearity under nonlinear boundary conditions. Computers & Mathematics with Applications, Vol. 74, Issue. 3, p. 360.

Ding, Juntang and Kou, Wei 2019. Blow-up solutions for reaction diffusion equations with nonlocal boundary conditions. Journal of Mathematical Analysis and Applications, Vol. 470, Issue. 1, p. 1.

Gladkov, Alexander and Guedda, Mohammed 2020. Influence of variable coefficients on global existence of solutions of semilinear heat equations with nonlinear boundary conditions. Electronic Journal of Qualitative Theory of Differential Equations, p. 1.

Tian, Huimin and Zhang, Lingling 2020. Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions. Open Mathematics, Vol. 18, Issue. 1, p. 1552.

Zhang, Huan and Fang, Zhong Bo 2020. Blow-up analysis for a nonlocal reaction-diffusion system with time-dependent coefficients. Applicable Analysis, Vol. 99, Issue. 6, p. 976.

Chung, Soon‐Yeong and Hwang, Jaeho 2021. Blow‐up solutions to nonlinear parabolic equations with non‐autonomous reactions under the mixed boundary conditions. Mathematical Methods in the Applied Sciences, Vol. 44, Issue. 7, p. 5560.

Xiaoyue, Zhang and Lingling, Zhang 2021. Analysis on blow-up time of parabolic equation system with nonlinear boundary conditions. p. 6651.

Li, Fan and Zhang, Lingling 2021. Blow-up phenomenon of parabolic equations with nonlocal terms under Neumann boundary conditions. p. 1.

Li, Jianjiao and Zhang, Lingling 2022. Analysis on blow-up time of parabolic equation system with nonlinear boundary conditions. p. 3174.

Yang, Yi and Fang, Zhong Bo 2022. On a strongly damped semilinear wave equation with time-varying source and singular dissipation. Advances in Nonlinear Analysis, Vol. 12, Issue. 1,

Kwon, Tae In and Fang, Zhong Bo 2022. Lower bounds for the blow-up time of a nonlocal reaction-diffusion system with time-dependent coefficients. Quaestiones Mathematicae, Vol. 45, Issue. 7, p. 1049.

王, 美丹 2023. Blow-Up Analysis of Divergent Reaction Diffusion Equations with Weighted Functions. Advances in Applied Mathematics, Vol. 12, Issue. 10, p. 4264.

Ding, Juntang and Pang, Wenjun 2023. Blow-up behavior for a degenerate parabolic systems subject to Neumann boundary conditions. Applicable Analysis, Vol. 102, Issue. 13, p. 3795.

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Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions

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