Geodesic
Existence and uniqueness of solutions for gradient systems without a compactness embedding condition
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 637-651.

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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.
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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     title = {Existence and uniqueness of solutions for gradient systems without a compactness embedding condition},
     journal = {Czechoslovak Mathematical Journal},
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Boussandel, Sahbi. Existence and uniqueness of solutions for gradient systems without a compactness embedding condition. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 637-651. doi : 10.21136/CMJ.2019.0416-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0416-17/

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