Existence of solutions for a nonlinear hyperbolic-parabolic equation in a non-cylinder domain (Q1907716)

Using the penalization technique of J.-L. Lions, the author proves existence of at least one solution to the mixed problem for the hyperbolic-parabolic equation \[ K_2 (x) u'' + K_1 (x) u' - \sum^n_{i,j = 1} {\partial \over \partial x_j} \left( a_{ij} (x,t) {\partial u \over \partial x_i} \right) + |u |^\rho u = f \] is an expanding with \(t\) noncylindrical domain.