Diffusion in partially fissured media and implicit evolution systems. (English) Zbl 0862.34047
As the authors show, a large class of models for flow in partially fissured porous media lead to abstract evolution equations of the form
\[
{d\over dt} A \bigl(u(t) \bigr)+ B \bigl(u(t) \bigr) \ni f(t),
\]
where \(A\) is a subgradient and \(B\) is maximal monotone on a product of three Hilbert spaces. The operator \(A\) is not necessarily compact in all its components, and this allows to analyze also problems related to fluid flows in fractured media. The existence and uniqueness of solutions for the Cauchy problem are established and sufficient conditions for continuous dependence of the solutions are given.
Reviewer: P.Renno (Napoli)
MSC:
34G20 | Nonlinear differential equations in abstract spaces |
37C10 | Dynamics induced by flows and semiflows |
34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
76S05 | Flows in porous media; filtration; seepage |