On the Cauchy problem for the evolution \(p\)-Laplacian equations with gradient term and source

DOI10.1016/j.jde.2006.11.014zbMath1128.35059OpenAlexW1997306252MaRDI QIDQ878545

Hongjun Yuan, Xiaojing Xu, Chunling Cao, Wen-jie Gao, Song Zhe Lian

Publication date: 26 April 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.11.014

zbMATH Keywords

blow-upglobal existencesmall initial datalarge initial data

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic equations (35K15)

Related Items (12)

Singular parabolic equations with measures as initial data ⋮ Classification of blowup solutions for a parabolic \(p\)-Laplacian equation with nonlinear gradient terms ⋮ The Cauchy problem for a parabolic \(p\)-Laplacian equation with combined nonlinearities ⋮ Cauchy problem for doubly singular parabolic equation with gradient source ⋮ Bifurcation diagrams of a \(p\)-Laplacian Dirichlet problem with Allee effect and an application to a diffusive logistic equation with predation ⋮ Critical exponents for the \(p\)-Laplace heat equations with combined nonlinearities ⋮ On the Cauchy problem for the singular parabolic equations with gradient term ⋮ Cauchy problem for doubly degenerate parabolic equation with gradient source ⋮ Liouville-type theorems for nonlinear degenerate parabolic equation ⋮ On the Cauchy problem for the evolution \(p\)-Laplacian equations with gradient term and source and measures as initial data ⋮ Unnamed Item ⋮ Blow-up analysis for parabolic \(p\)-Laplacian equations with a gradient source term

Cites Work

• Degenerate parabolic equations
• Nonexistence of global weak solutions for classes of nonlinear wave and parabolic equations
• Asymptotic stability and blowing up of solutions of some nonlinear equations
• Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source
• On solutions of some doubly nonlinear degenerate parabolic equations with absorption
• Blow up of positive solutions for a family of nonlinear parabolic equations in general domain in \(\mathbb{R}^N\)
• On the Cauchy problem and initial traces for the evolution \(p\)-Laplacian equations with strongly nonlinear sources
• Existence and nonexistence of global solutions for nonlinear parabolic equations
• Hölder estimates for nonlinear degenerate parabolic sytems.
• Some Blowup Results for a Nonlinear Parabolic Equation with a Gradient Term
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the Cauchy problem for the evolution \(p\)-Laplacian equations with gradient term and source