Czechoslovak Mathematical Journal, Vol. 69, No. 3, pp. 637-651, 2019


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

Sahbi Boussandel

Received September 5, 2017.   Published online June 20, 2019.

Abstract:  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.
Keywords:  gradient system; existence and uniqueness of solution; Galerkin method; quadratic form; weakly lower semicontinuity; diffusion equation
Classification MSC:  35F20, 35F25, 35F30, 35K57, 47H05, 47J05
DOI:  10.21136/CMJ.2019.0416-17


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Affiliations:   Sahbi Boussandel, Université de Carthage, Faculté des Sciences de Bizerte, LR03ES04 Laboratoire EDP et Applications, 7021, Jarzouna, Tunisia, e-mail: sboussandels@gmail.com


 
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