On Parabolic Variational Inequalities with Multivalued Terms and Convex Functionals
In this paper, we consider the following parabolic variational inequality containing a multivalued term and a convex functional: Find u ϵ Lp(0, T;W1,p0 (Ω)) and f ϵ F(., ., u) such that u(., 0) = u0 and (ut + Au, v - u) + ψ(v) - ψ(u) ≥ ∫ Q f(v - u) dx dt for all v ϵ Lp(0, T;W1,p0 (Ω)), where A is the principal term; F is a multivalued lower-order term; ψ(u) = ∫T0 ψ(t, u) dt is a convex functional. Moreover,we study the existence and other properties of solutions of this inequality assuming certain growth conditions on the lower-order term F.
V. K. Le and K. Schmitt, "On Parabolic Variational Inequalities with Multivalued Terms and Convex Functionals," Advanced Nonlinear Studies, vol. 18, no. 2, pp. 269-287, Walter de Gruyter GmbH, Apr 2018.
The definitive version is available at https://doi.org/10.1515/ans-2018-0004
Mathematics and Statistics
Keywords and Phrases
Convex Functional; Extremal Solutions; Multivalued Term; Sub-supersolutions; Variational Inequalities
International Standard Serial Number (ISSN)
Article - Journal
© 2018 Walter de Gruyter GmbH, All rights reserved.
01 Apr 2018