Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory

Abstract

In the paper, we focus on the local existence and blow-up of solutions for a time fractional nonlinear equation with biharmonic operator and exponentional nonlinear memory in an Orlicz space. We first establish a $ L^p-L^q $ estimate for solution operators of a time fractional nonlinear biharmonic equation, and obtain bilinear estimates for mild solutions. Then, based on the contraction mapping principle, we establish the local existence of mild solutions. Moreover, by using the test function method, we obtain the blow-up result of solutions.

Keywords

• fractional biharmonic equation
• exponentional nonlinear memory
• blow-up
• local existence