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Existence and uniqueness of solutions for gradient systems without a compactness embedding condition. (English) Zbl 1513.35121

Summary: This paper is devoted to the existence and uniqueness of solutions for gradient systems of evolution which involve gradients taken with respect to time-variable inner products. The Gelfand triple \((V,H,V')\) considered in the setting of this paper is such that the embedding \(V\hookrightarrow H\) is only continuous.

MSC:

35F20 Nonlinear first-order PDEs
35F25 Initial value problems for nonlinear first-order PDEs
35F30 Boundary value problems for nonlinear first-order PDEs
35K57 Reaction-diffusion equations
47H05 Monotone operators and generalizations
47J05 Equations involving nonlinear operators (general)
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