Blow-Up Results for a Class of Quasilinear Parabolic Equation with Power Nonlinearity and Nonlocal Source

Abstract

This paper deals with a class of quasilinear parabolic equation with power nonlinearity and nonlocal source under homogeneous Dirichlet boundary condition in a smooth bounded domain; we obtain the blow-up condition and blow-up results under the condition of nonpositive initial energy.

Note on blow up solutions for a general class of semilinear parabolic equations involving second order operator

“…We provide the reader to the literature [3,6] and [11], for some recent interesting research on the local reactiondiffusion equation with non local boundary conditions we can refer to [9]. Inspired by the above mentioned papers, especially from [3] and [13], we discuss the blow-up solutions of the following initial-boundary value problem of p-Laplacian parabolic equation:…”

“…Blow-up phenomena for this kind of problems in bounded domains have been extensively studied. Concavity method has been used so far to derive the blow-up solutions for some variants of the equations (1.1), see [1,6,8,13]. By using the concavity method, Philippin and Proytcheva, in [10], obtained the blow-up solutions for problem (1.1) (with h = id) under the conditions:…”