Destruction of solutions for class of wave p(x)−bi-Laplace equation with nonlinear dissipation

Abstract

An initial value problem is considered for the nonlinear dissipative wave equation containing the p(x)-bi-Laplacian operator. For this problem, sufficient conditions for the blow-up with nonpositive initial energy of a generalized solution are obtained in finite time where a wide variety of techniques are used.

Keywords

• sobolev spaces with variable exponents
• p(x)-bi-laplace
• blow-up
• initial energy