Blow-Up, Exponential Grouth of Solution for a Nonlinear Parabolic Equation with p(x) - Laplacian

Ouaoua, Amar; Maouni, Messaoud

doi:10.28924/2291-8639-17-2019-620

Research Article

Blow-Up, Exponential Grouth of Solution for a Nonlinear Parabolic Equation with p(x) - Laplacian

Amar Ouaoua¹*
Messaoud Maouni¹

Laboratory of Applied Mathematics and History and Didactics of Mathematiccs (LAMAHIS), University of 20 August 1955, Skikda, Algeria.

* Corresponding author

Abstract

In this paper, we consider the following equation

$u_{t}-\func{div}\left( \left\vert \nabla u\right\vert ^{p\left( x\right)-2}\nabla u\right) +\omega \left\vert u\right\vert ^{m\left( x\right)-2}u_{t}=b\left\vert u\right\vert ^{r\left( x\right) -2}u.$

We prove a finite time blowup result for the solutions in the case $\omega =0$ and exponential growth in the case $\omega >0$, with the negative initial energy in the both case.

How to Cite

A. Ouaoua, M. Maouni, Blow-Up, Exponential Grouth of Solution for a Nonlinear Parabolic Equation with p(x) - Laplacian, Int. J. Anal. Appl. 17 (2019), 620–629. https://doi.org/10.28924/2291-8639-17-2019-620

BibTeX

@article{Ouaoua2019,
  author  = {Ouaoua, Amar and Maouni, Messaoud},
  title   = {Blow-Up, Exponential Grouth of Solution for a Nonlinear Parabolic Equation with p(x) - Laplacian},
  journal = {Int. J. Anal. Appl.},
  volume  = {17},
  year    = {2019},
  pages   = {620--629},
  doi     = {10.28924/2291-8639-17-2019-620}
}

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