Extremality in Solving General Quasilinear Parabolic Inclusions

S. Carl and D. Motreanu
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S. Carl: Martin-Luther-Universität Halle-Wittenberg
D. Motreanu: Université de Perpignan

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 3, No 1, 463-477

Abstract: Abstract The paper deals with an initial boundary-value problem for a parabolic inclusion whose multivalued term has the structure of a difference between the Clarke generalized gradient of some locally Lipschitz function verifying a unilateral growth condition and the subdifferential of a convex function, and where the elliptic part is expressed by a general quasilinear operator of the Leray-Lions type. Our results address not only the existence of solutions, but also the extremality inside an order interval determined by appropriately defined upper and lower solutions as well as the compactness of the solution set in suitable spaces.

Keywords: Quasilinear parabolic inclusions; extremal solutions; upper and lower solutions; generalized gradients; nonsmooth analysis (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s10957-004-5718-z

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