We consider a class of strictly pseudohyperbolic equations with lower order terms. The solvability the Cauchy problem in Sobolev spaces special weights is established. uniqueness solution proven and estimates are obtained.

Abstract We study the regularity of interface for optimal energy configurations functionals involving bulk energies with an additional perimeter penalization interface. Here we allow a more general structure functional in term. For minimal configuration ( E , u str...

Abstract We consider a Cauchy–Dirichlet problem for quasilinear second order parabolic equation with lower term driven by singular coefficient. establish an existence result to such and we describe the time behavior of solution in case infinite–time horizon.