Weak Solutions of Initial-Boundary Value Problems for Class of Nonlinear Viscoelastic Equations

Existence and uniqueness theorems are established for initial-boundary value problems corresponding to the equation [formula ommited]= g under assumptions on P and a that include as special cases the isentropic gas law P(v) = v-γ with γ \u3e 1 with α(v) = v-1 along with generalizations that allow for Non convex P. The smoothness assumptions made on P and a are much weaker then are usual in studying these problems and the initial data is only required to satisfy u(-,0)εW1∞ (0,1) and u t (*,0)εL2 (0,1). © 1987, Taylor & Francis Group, LLC. All rights reserved