Extinction and positivity of the solutions of the heat equations with absorption on networks

DOI10.1016/j.jmaa.2011.03.006zbMath1219.35024OpenAlexW2013534114MaRDI QIDQ536267

Young-Su Lee, Soon-Yeong Chung, Yun-Sung Chung

Publication date: 16 May 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.03.006

zbMATH Keywords

nontrivial solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Semilinear parabolic equations (35K58) Positive solutions to PDEs (35B09)

Related Items (23)

\(p\)-th Kazdan-Warner equation on graph in the negative case ⋮ Blowup Behavior of Solutions to an $\omega$-diffusion Equation on the Graph ⋮ A complete characterization of extinction versus positivity of solutions to a parabolic problem of \(p\)-Laplacian type in graphs ⋮ The existence and nonexistence of global solutions for a semilinear heat equation on graphs ⋮ A new condition for blow-up solutions to discrete semilinear heat equations on networks ⋮ Blow-up in a network mutualistic model ⋮ Global stability in a networked SIR epidemic model ⋮ Extinction and asymptotic behavior of solutions for the \(\omega\)-heat equation on graphs with source and interior absorption ⋮ Extinction and positivity of the solutions for a \(p\)-Laplacian equation with absorption on graphs ⋮ Blow-up solutions and global solutions to discrete \(p\)-Laplacian parabolic equations ⋮ Positive solutions of \(p\)-th Yamabe type equations on graphs ⋮ EXISTENCE OF GLOBAL SOLUTIONS TO SOME NONLINEAR EQUATIONS ON LOCALLY FINITE GRAPHS ⋮ Stability of Turing bifurcation in a weighted networked reaction-diffusion system ⋮ Extinction and positivity for the evolution \(p\)-Laplacian equations with absorption on networks ⋮ A weighted networked SIRS epidemic model ⋮ A complete characterization of nonlinear absorption for the evolution \(p\)-Laplacian equations to have positive or extinctive solutions ⋮ Convergence of ground state solutions for nonlinear Schrödinger equations on graphs ⋮ \(p\)-Laplacian equations on locally finite graphs ⋮ Blow-up problems for nonlinear parabolic equations on locally finite graphs ⋮ Critical blow-up and global existence for discrete nonlinear \(p\)-Laplacian parabolic equations ⋮ On-diagonal lower estimate of heat kernels for locally finite graphs and its application to the semilinear heat equations ⋮ MONOTONICITY AND ASYMPTOTIC PROPERTIES OF SOLUTIONS FOR PARABOLIC EQUATIONS VIA A GIVEN INITIAL VALUE CONDITION ON GRAPHS ⋮ Blow-up for the ω-heat equation with Dirichlet boundary conditions and a reaction term on graphs

Cites Work

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• [https://portal.mardi4nfdi.de/wiki/Publication:4337503 Open problems of Paul Erd�s in graph theory]
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