Existence via time discretization for a class of doubly nonlinear operator-differential equations of Barenblatt-type

The initial value problem for a first order operator-differential equation of type M(u′)+A(u,u′)=f is studied, where both M and A are nonlinear operators. The equation can be interpreted as the quasistatic limit of a second order evolution equation with a severe coupling of the damping and nondamping term. Existence of a global-in-time weak solution is shown by proving convergence of a suitable time discretization method.