On solutions of semilinear wave equations

Abstract

under the first initial-boundary condition and prove the existence of functions which exist for every t 3 0 and solve the equations in a sense defined in this paper and for some classes of equations with the first order dissipation we find an unbounded set in a subspace of [L2(Q)12 with a property that if initial value belongs to it, then the equation has a global classical solution. Let (x, t) be a space-time variable in IR” X [0, 03). Let us consider the following semilinear wave equations