Calculus of Variations and Geometric Measure Theory
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F. Paronetto

Existence results for a class of evolution equations of mixed type

created on 11 Sep 2002
modified on 31 Oct 2003

[BibTeX]

Submitted Paper

Inserted: 11 sep 2002
Last Updated: 31 oct 2003

Year: 2002

Abstract:

We give an existence result for the evolution equation $(R u)' + A u = f$ in the space $W = \{ u \in V \
\ (R u)' \in V' \}$ where $V$ is a Banach space and $R$ is a non-invertible operator (the equation may be partially elliptic and partially parabolic, both forward and backward) and we study the ``Cauchy-Dirichlet'' problem associated to this equation (indeed also for the inclusion $(R u)' + A u \ni f$). We also investigate continuous and compact embeddings of $W$ and regularity in time of the solution. At the end we give some examples of different $R$.


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