Existence of solutions for anisotropic parabolic Ni-Serrin type
equations originated from a capillary phenomena with nonstandard growth
nonlinearity.
Abstract
We consider an initial boundary value problem for a class of anisotropic
parabolic Ni-Serrin type equations with nonstandard nonlinearity in a
bounded smooth domain with homogeneous Dirichlet boundary condition.
Because the nonlinear perturbation leads to difficulties (it does not
have a definite sign) in obtaining a priori estimates in the energy
method, we had to modify the Tartar method significantly. Under suitable
assumptions, we obtain the global existence, decay, and extinction of
solutions.