Differential and Integral Equations

Local and global existence for evolutionary p-Laplacian equation with nonlocal source

Haifeng Shang and Mengmeng Song

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Abstract

This paper examines the existence and nonexistence of solutions on the Cauchy problem for the evolutionary p-Laplacian equation with nonlocal source. By a priori estimates, we establish the local existence, global existence and nonexistence of solutions for that Cauchy problem. In particular, a Fujita's type critical exponent is obtained, which extends several classical results to the problem considered here.

Article information

Source
Differential Integral Equations, Volume 32, Number 3/4 (2019), 139-168.

Dates
First available in Project Euclid: 23 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1548212427

Mathematical Reviews number (MathSciNet)
MR3909982

Zentralblatt MATH identifier
07036979

Subjects
Primary: 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations 35K65: Degenerate parabolic equations 35B33: Critical exponents

Citation

Shang, Haifeng; Song, Mengmeng. Local and global existence for evolutionary p-Laplacian equation with nonlocal source. Differential Integral Equations 32 (2019), no. 3/4, 139--168. https://projecteuclid.org/euclid.die/1548212427


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