1,463 research outputs found
Multi-valued, singular stochastic evolution inclusions
We provide an abstract variational existence and uniqueness result for
multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert
spaces with general additive and Wiener multiplicative noise. As examples we
discuss certain singular diffusion equations such as the stochastic 1-Laplacian
evolution (total variation flow) in all space dimensions and the stochastic
singular fast diffusion equation. In case of additive Wiener noise we prove the
existence of a unique weak-* mean ergodic invariant measure.Comment: 39 pages, in press: J. Math. Pures Appl. (2013
Evolutionary Oseen model for generalized Newtonian fluid with Multivalued Nonmonotone Friction Law
The paper deals with the non-stationary Oseen system of equations for the generalized Newtonian incompressible fluid with multivalued and nonmonotone frictional slip boundary conditions. First, we provide a result on existence of a unique solution to an abstract evolutionary inclusion involving the Clarke subdifferential term for a nonconvex function. We employ a method based on a surjectivity theorem for multivalued L-pseudomonotone operators. Then, we exploit the abstract result to prove the weak unique solvability of the Oseen system
CONVERGENCE ANALYSIS FOR APPROXIMATING SOLUTION OF VARIATIONAL INCLUSION PROBLEM
This article aims to define a new resolvent operator for variational inclusion problems in the framework of Banach spaces. We design a rapid algorithm using the resolvent operator to approximate the solution of the variational inclusion problem in Banach spaces. Additionally, we show that the algorithm articulated in this article converges faster than the well-known and notable algorithm due to Fang and Huang. To show the superiority and prevalence of the obtained results, we propound a numerical and computational example upholding our claim. Lastly, a minimization problem is solved with the help of the proposed algorithm, which is the first attempt in the current context of the study
Convergence of Rothe scheme for hemivariational inequalities of parabolic type
This article presents the convergence analysis of a sequence of piecewise
constant and piecewise linear functions obtained by the Rothe method to the
solution of the first order evolution partial differential inclusion
, where the multivalued term
is given by the Clarke subdifferential of a locally Lipschitz functional. The
method provides the proof of existence of solutions alternative to the ones
known in literature and together with any method for underlying elliptic
problem, can serve as the effective tool to approximate the solution
numerically. Presented approach puts into the unified framework known results
for multivalued nonmonotone source term and boundary conditions, and
generalizes them to the case where the multivalued term is defined on the
arbitrary reflexive Banach space as long as appropriate conditions are
satisfied. In addition the results on improved convergence as well as the
numerical examples are presented.Comment: to appear in: International Journal of Numerical Analysis and
Modelin
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