Existence and uniqueness of solutions for gradient systems without a compactness embedding condition

Boussandel, Sahbi

Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 637-651

Abstract (VO)

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.

Détail

DOI : 10.21136/CMJ.2019.0416-17

Classification : 35F20, 35F25, 35F30, 35K57, 47H05, 47J05
Keywords: gradient system; existence and uniqueness of solution; Galerkin method; quadratic form; weakly lower semicontinuity; diffusion equation

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