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2015 | 13 | 1 |
Tytuł artykułu

Parabolic variational inequalities with generalized reflecting directions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-07-17
zaakceptowano
2015-10-08
online
2015-12-02
Twórcy
  • 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
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