Young measure solutions for the wave equation with p(x, t)-Laplacian: Existence and blow-up

We consider the Dirichlet problem u(tt) = Lu + f (x, t), (x, t) E Q(T) = Q x (0, T), Lu = div (a(x, t) vertical bar del u vertical bar(p(x,t)-2) del u) + b(x, t) vertical bar u vertical bar(sigma(x,t)-2) u u(x, 0) = u(0)(x), u(t)(x, 0) = U-1 (x), x is an element of Omega, u vertical bar(Gamma T) = 0, Gamma(T) = theta Omega x (0, T), where the coefficients a(x, t), b(x, t), f (x, t) and the exponents of nonlinearities p(x, t), sigma (x, t) are given functions. We prove local and global existence and blow-up of Young measure solutions. We construct Young measure solutions as the limit of the sequence of solutions of the regularized equations u(tt) = Lu + div(epsilon del u(t)) + f(x, t). (C) 2013 Elsevier Ltd. All rights reserved.