On the Global Nonexistence of a Solution for Wave Equations with Nonlinear Memory Term

Abstract

The paper is devoted to the problem of the local existence for a solution to a nonlinear wave equation, with the dissipation given by a nonlinear form with the presence of a nonlinear memory term. Moreover, the global nonexistence of a solution is established using the test function method. We combine the Fourier transform and fractional derivative calculus to achieve our goal.

Keywords

• Lyapunov functions
• wave equations
• well-posedness
• nonlinear memory term
• exponential
• multiplier method