Blow up at finite time for wave equation in visco-elasticity: a new kind for one spatial variable Emden-Fowler type

TL;DR

This paper investigates a nonlinear wave equation of Emden-Fowler type with visco-elastic effects, demonstrating finite-time blow-up of solutions under specific conditions, highlighting the dissipative influence of the visco-elastic term.

Contribution

It introduces a new nonlinear wave equation model with visco-elastic effects and proves finite-time blow-up results for solutions in the one-dimensional setting.

Findings

Solutions blow up in finite time under certain initial conditions.

Visco-elastic term induces dissipative behavior in the wave equation.

Global solutions do not exist in L2 space for the considered problem.

Abstract

For one spatial variable, a new kind of nonlinear wave equation for Emden-Fowler type is considered with boundary value null and initial values. Under certain conditions on the initial data and the exponent p, we exhibit that the visco-elastic term leads our problem to be dissipative and the global solutions still non-exist in L2 at given finite time.