Asymptotic behavior for a fourth-order parabolic equation modeling thin film growth

DOI10.1016/j.aml.2017.11.015zbMath1383.65109OpenAlexW2768794430MaRDI QIDQ1693649

Chengyuan Qu, Bo Liang, Wen-Shu Zhou

Publication date: 31 January 2018

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2017.11.015

zbMATH Keywords

asymptotic behaviorfourth-order parabolic equationnonstandard growth conditionblow-up time estimate

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Weak solutions to PDEs (35D30) Blow-up in context of PDEs (35B44)

Related Items (8)

Singular solutions in a \(p(x)\)-Laplace equation with multi-sources ⋮ Singular solutions for the fourth‐order parabolic equation with nonstandard growth conditions and absorption ⋮ Classification of singular solutions in a nonlinear fourth-order parabolic equation ⋮ Note on a higher order pseudo‐parabolic equation with variable exponents ⋮ Energy classification in a nonstandard fourth‐order parabolic equation with a Navier boundary condition ⋮ Asymptotic behavior of global solutions to a class of mixed pseudo-parabolic Kirchhoff equations ⋮ Unnamed Item ⋮ Singular properties of solutions for a parabolic equation with variable exponents and logarithmic source

Cites Work

• Blow-up of solutions to parabolic equations with nonstandard growth conditions
• Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy
• Upper bound estimate for the blow-up time of an evolution \(m\)-Laplace equation involving variable source and positive initial energy
• The blow-up of solutions for \(m\)-Laplacian equations with variable sources under positive initial energy
• Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source
• Sharp threshold for blow-up and global existence in a semilinear parabolic equation with variable source
• Blow-up in a semilinear parabolic problem with variable source under positive initial energy

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