On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities
The paper concerns with a mixed problem for the following quasilinear hyperbolic equation with a strong damping \[ u_{tt} - \nabla(|\nabla u|^{p-2} \nabla u) - \Delta u_t + \Xi = f, \] where \( \Xi(t,x) \in \varphi(u'(t,x)) \) and \( \varphi\) is a discontinuous nonlinear set valued mapping. The existence of global weak solutions as well as the asymptotic behavior of them are studied.
scientific article; zbMATH DE number 2003972