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Parabolic variational inequalities with generalized reflecting directions

100%

Rotenstein E.

Open Mathematics

2015

tom 13

nr 1

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.

Numerical schemes for multivalued backward stochastic differential systems

63%

Maticiuc L., Rotenstein E.

Open Mathematics

2012

tom 10

nr 2

693-702

We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: $$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$ where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational inequality in conjunction with Yosida approximation techniques.

Ograniczanie wyników

2 Open Mathematics

2 Rotenstein E.

1 Maticiuc L.

1 2015

1 2012

Wyniki wyszukiwania

Parabolic variational inequalities with generalized reflecting directions

Numerical schemes for multivalued backward stochastic differential systems