Asymptotic Behavior and Decay Estimates of the Solutions for a Nonlinear Parabolic Equation with Exponential Nonlinearity

Abstract

We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and mild solutions, we derive decay estimates and the asymptotic behavior for small global-in-time solutions.

References in corpus (1)

• Asymptotics for a nonlinear integral equation with a generalized heat kernel

Cited by in corpus (2)

• On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative
• Fractional semilinear heat equations with singular and nondecaying initial data