Blow-Up Time of Solutions for a Parabolic Equation with Exponential Nonlinearity

Abstract

This paper studies a parabolic equation with exponential nonlinearity, which has several applications, for example the self-trapped beams in plasma. Based on a modified concavity method we prove the blow-up of the solution for initial data with high initial energy. We also proposed the solution’s lower and upper bound of the blow-up time for the equation. Our results complement the existing results.

Keywords

• parabolic equation
• exponential nonlinearity
• blow-up