Global existence and uniform energy decay rates for the semilinear parabolic equation with a memory term and mixed boundary condition

DOI10.1155/2013/532935zbMath1293.35145OpenAlexW2014233904WikidataQ58917055 ScholiaQ58917055MaRDI QIDQ2015712

Zhong Bo Fang, Liru Qiu

Publication date: 23 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/532935

zbMATH Keywords

Lyapunov functiongeneralized Lewis functions

Mathematics Subject Classification ID

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

Related Items (7)

Blow-up of solutions to a viscoelastic parabolic equation with positive initial energy ⋮ Mittag-Leffler stability for a fractional Euler-Bernoulli problem ⋮ Optimal control of a parabolic equation with memory ⋮ General decay rate estimates for a semilinear parabolic equation with memory term and mixed boundary condition ⋮ Blow-up of solutions to a semilinear heat equation with a viscoelastic term and a nonlinear boundary flux ⋮ Qualitative analysis for a reaction-diffusion predator-prey model with disease in the prey species ⋮ A general decay result for a semilinear heat equation with past and finite history memories

Cites Work

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• A general decay result in a quasilinear parabolic system with viscoelastic term
• Existence and regularity for a class of integrodifferential equations of parabolic type
• Mathematics in industrial problems. Part 5
• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• The reaction-diffusion equation with Lewis function and critical Sobolev exponent
• On Parabolic Volterra Equations in Several Space Dimensions
• Weak And Classical Solutions Of Some Nonlinear Volterra Integrodifferential Equations
• BLOW UP OF SOLUTIONS WITH POSITIVE INITIAL ENERGY FOR THE NONLOCAL SEMILINEAR HEAT EQUATION

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