Warianty tytułu
Języki publikacji
Abstrakty
We study, in a Hilbert framework, some abstract parabolic variational inequalities, governed by reflecting subgradients with multiplicative perturbation, of the following type: y´(t)+ Ay(t)+0.t Θ(t,y(t)) ∂φ(y(t))∋f(t,y(t)),y(0) = y0,t ∈[0,T] where A is a linear self-adjoint operator, ∂φ is the subdifferential operator of a proper lower semicontinuous convex function φ defined on a suitable Hilbert space, and Θ is the perturbing term which acts on the set of reflecting directions, destroying the maximal monotony of the multivalued term. We provide the existence of a solution for the above Cauchy problem. Our evolution equation is accompanied by examples which aim to (systems of) PDEs with perturbed reflection.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Opis fizyczny
Daty
otrzymano
2015-07-17
zaakceptowano
2015-10-08
online
2015-12-02
Twórcy
autor
-
Faculty of Mathematics, "Alexandru Ioan Cuza" University of Iaşi, 9 Carol I Blvd.,
700506, Iaşi, România
Bibliografia
- [1] Gassous, A; Răşcanu. A; Rotenstein, E. - Stochastic variational inequalities with oblique subgradients, Stoch. Proc. Appl., 2012,Volume 122, Issue 7, 2668-2700.
- [2] Răşcanu, A.; Rotenstein, E. - A non-convex setup for multivalued differential equations driven by oblique subgradients, NonlinearAnal.-Theor., 2014, Volume 111 (December), 82-104.[WoS]
- [3] Lions, P.-L.; Sznitman, A. - Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 1984,Volume 37, no. 4, 511-537.
- [4] Barbu, V.; Răşcanu, A. - Parabolic variational inequalities with singular input, Differ. Integral Equ., 1997, Volume 10, Number 1,pp. 67-83.
- [5] Răşcanu, A. - Deterministic and stochastic differential equations in Hilbert spaces involving multivalued maximal monotoneoperators, Panamer. Math. J., 1996, Volume 6, no. 3, 83-119.
- [6] Pardoux, E.; Răşcanu, A. - Stochastic Differential Equations, Backward SDEs, Partial Differential Equations, Stochastic Modellingand Applied Probability, vol. 69, Springer, 2014.
- [7] Răşcanu, A.; Rotenstein, E. - The Fitzpatrick function-a bridge between convex analysis and multivalued stochastic differentialequations, J. Convex Anal., 2011, Volume 18 (1), 105-138.
- [8] Eidus, D. - The perturbed Laplace operator in a weighted L2-space, J. Funct. Anal., 1991, Volume 100, no. 2, 400-410.
- [9] Barbu, V.; Favini, A. - On some degenerate parabolic problems, Ricerche Mat., 1997, Volume 46, Number 1, 77-86.
- [10] Altomare, F.; Milella, S.; Musceo, G. - Multiplicative perturbations of the Laplacian and related approximation problems, J. Evol.Equ., 2011, 11, 771-792.[WoS][Crossref]
- [11] Barbu, V. - Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer, 2010.
- [12] Lions, J.L. - Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, 1969.
- [13] Barbu, V. - Optimal Control of Variational Inequalities, Pitman Publishing INC., 1984.
- [14] Aubin, J. P. - Un théorème de compacité, C. R. Acad. Sci. Paris, 1963, 256, 5042-5044.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0083