Existence and convergence theorems for doubly nonlinear partial differential equations of elliptic-parabolic type (Q1813224)

The author proves the existence of weak solutions of the following initial-boundary value problem for the equations of the form \((\partial/\partial t)\alpha(u)-\sum^ N_{i=1}(\partial/\partial x_ i)\beta_ i(x,t,u,\nabla_ xu)\ni f(x,t)\) in \(G\times(0,T)\), \(u=0\) on \(\partial G\times(0,T)\), \(\alpha(u)|_{t=0}\ni v_ 0(x)\) on \(G\), where \(\alpha\) is a maximal monotone graph in \(\mathbb{R}\times\mathbb{R}\). This result is derived using the regularization of this problem.