Lower bounds for blow-up time in a nonlinear parabolic problem with a gradient nonlinearity


Mashiyev R. A. , Ekincioglu İ.

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s41808-022-00147-y
  • Journal Name: JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS
  • Journal Indexes: Emerging Sources Citation Index, Scopus
  • Keywords: Nonlinear parabolic problem, Gradient nonlinearity, Blow-up time, Lower bounds, Nonblow-up, EQUATIONS

Abstract

In this article, we study the blow-up properties of solutions to a parabolic problem with a gradient nonlinearity under homogeneous Dirichlet boundary conditions. By constructing an auxiliary function and by modifying the first order differential inequality, we obtain lower bounds for the blow-up time of solutions in L-k (Omega) (k > 1) norm and conditions which ensure that blow-up cannot occur.