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Characterization of a class of evolution operators generated by time- dependent subdifferentials. (English) Zbl 0689.35048
Various conditions on the time-dependence of subdifferentials (or of convex functions) have been introduced to solve the Cauchy problem for the evolution equation generated by the time-dependent subdifferentials. A condition, which is implicit in those cases ever considered, on the time-dependence of subdifferentials is introduced in this paper. And it is shown that this condition is necessary and sufficient in order that the Cauchy problem admits a unique solution satisfying a certain type of energy inequality.
Reviewer: M.Kubo

35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
47J05 Equations involving nonlinear operators (general)
34G20 Nonlinear differential equations in abstract spaces