Existence via time discretization for a class of doubly nonlinear operator-differential equations of Barenblatt-type
The authors study the initial value problem for a first order operator-differential equation \(M(u')+A(u,u')=f\), where the unknown function \(u=u(t)\) takes values in a reflexive separable Banach space and \(M:V\to V'\), \(A:V\times V\to V'\) are nonlinear operators. Under some structural assumptions, the authors establish existence of a global weak solution to this problem by proving convergence of a suitable time discretization method. Applications are given to partial differential equations of Barenblatt type.
scientific article; zbMATH DE number 6140826