Variational formulation and structural stability of monotone equations
This very informative and well-written paper pertains to the author's ongoing research program which concerns the variational representation of nonlinear evolutionary partial differential equations and the application of variational methods to the analysis of the structural stability of such equations. It consists of three parts. The first one (Sections 1--3) provides an outline, as well as several pertinent examples, of the Fitzpatrick theory regarding monotone operators and their representative functions. The second part (Sections 4--6) is devoted to the \(\Gamma\)-convergence of representative functions. In the third part (Sections 7--9) of the paper, the author uses his previous results to study periodic (Section 7) and initial-value (Section 8) monotone flows. The possible onset of long memory in the limit is discussed in Section 9.
scientific article; zbMATH DE number 6161252
scientific article