Distributed systems of {PDE} in Hilbert space
John D. Cook, Ralph E. Showalter · Differential and Integral Equations · 1993
We present a system of two nonlinear evolution equations and a corresponding approximating system which provide a common framework for studying distributed microstructure models and a variety of other models for transport and diffusion in heterogeneous media.Existence and uniqueness are demonstrated using semigroup methods, and solutions to the approximating system are shown to converge strongly to the solution of the limiting system.In the microstructure case, new results are obtained, and additional PDE examples are provided to show that in general, certain hypotheses cannot be removed.