Extinction and asymptotic behavior of solutions for the \(\omega\)-heat equation on graphs with source and interior absorption

DOI10.1016/j.jmaa.2015.10.024zbMath1331.35355OpenAlexW1792177787MaRDI QIDQ892310

Kewang Chen, Jun Yu, Wenjun Liu

Publication date: 18 November 2015

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.2015.10.024

zbMATH Keywords

asymptotic behaviorextinction\(\omega\)-heat equationcritical extinction exponent

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Critical exponents in context of PDEs (35B33) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (14)

BLOW-UP PROBLEMS FOR GENERALIZED FUJITA-TYPE EQUATIONS ON GRAPHS ⋮ A condition for blow-up solutions to discrete semilinear wave equations on networks ⋮ 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 ⋮ On the critical set for Fujita type blow-up of solutions to the discrete Laplacian parabolic equations with nonlinear source on networks ⋮ Critical extinction exponent for a doubly degenerate non-divergent parabolic equation with a gradient source ⋮ Exponential energy decay of solutions for a transmission problem with viscoelastic term and delay ⋮ Convergence of ground state solutions for nonlinear Schrödinger equations on graphs ⋮ Existence and convergence of solutions for nonlinear biharmonic equations on graphs ⋮ Quenching of the solution to the discrete heat equation with logarithmic type sources on graphs ⋮ \(p\)-Laplacian equations on locally finite graphs ⋮ Blow-up problems for nonlinear parabolic equations on locally finite graphs ⋮ MONOTONICITY AND ASYMPTOTIC PROPERTIES OF SOLUTIONS FOR PARABOLIC EQUATIONS VIA A GIVEN INITIAL VALUE CONDITION ON GRAPHS

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