Czechoslovak Mathematical Journal, Vol. 69, No. 3, pp. 637-651, 2019
Existence and uniqueness of solutions for gradient systems without a compactness embedding condition
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