Abstract
This paper is devoted to the study of perturbation evolution problems involving time-dependent m-accretive operators. We present for a specific class of m-accretive operators with convex weakly compact-valued perturbation, some results about the existence of absolutely continuous solutions and BRVC solutions. We finish by giving several applications to various domains such as relaxation results, second-order evolution inclusions, fractional-order equations coupled with m-accretive operators and Skorohod differential inclusions.
Highlights
In the present paper, we are mainly interested in the study of the perturbed evolution problem governed by a time-dependent m-accretive operator A(t) − du dν (t) ∈ A(t, u(t)) +f (t, u(t)), ν a.e t [0, T]. (1)Here ν is a given positive Radon measure on [0, T], u : [0, T] → E is a right continuous function with density of du bounded variation, with respect to ν, t du →is its A(t) differential measure : D(A(t)) → 2E is a or Stieltjes measure, du dν is the time-dependent m-accretive operator, f : [0, T] × E → E is a Caratheodory mapping
We present several new variants in the study of absolutely continuous and bounded variation and right continuous (BVRC) solutions for (1) with time-dependent m-accretive operator A(t) and weakly compact-valued perturbation F
This leads to some remarkable applications such as periodic solutions, relaxation problems, second-order evolution driven with m-accretive operators with perturbation, fractional-order equation coupled with m-accretive operators, functional differential inclusion governed by m-accretive operators, sweeping process, and Skorohod differential inclusions
Summary
We are mainly interested in the study of the perturbed evolution problem governed by a time-dependent m-accretive operator A(t). It is important to know a few significant classes of m-accretive operators for which existence of absolutely continuous or bounded variation and right continuous (BVRC) solutions to (1) are proved In this regard, we present several new variants in the study of absolutely continuous and BVRC solutions for (1) with time-dependent m-accretive operator A(t) and weakly compact-valued perturbation F. We present several new variants in the study of absolutely continuous and BVRC solutions for (1) with time-dependent m-accretive operator A(t) and weakly compact-valued perturbation F This leads to some remarkable applications such as periodic solutions, relaxation problems, second-order evolution driven with m-accretive operators with perturbation, fractional-order equation coupled with m-accretive operators, functional differential inclusion governed by m-accretive operators, sweeping process, and Skorohod differential inclusions. They make it possible to obtain concrete solutions in various domains such as elastoplasticity, mechanics, traffic equilibria, and social and economic models
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