Existence and Uniqueness of Asymptotic Solution of a Semilinear Parabolic System with Measure Data Using BSDEs Approach

Year 2022, Volume: 10 Issue: 1, 11 - 29, 15.04.2022

Deborah Danıel

Abstract

This paper considers the existence and uniqueness of an asymptotic solution of a monotone semilinear parabolic system in divergence form with measure data. The proof of the main result is probabilistic, which are those of stochastic analysis, Markov process and primarily Backward Stochastic Differential Equations (BSDEs). The probabilistic solution to the system is considered as some generalization of the notion of renormalized (or entropy) solution. It is shown for a Cauchy-Dirichlet problem of a monotone semilinear parabolic system in divergence form with measure data, there exists a unique probabilistic solution of the system under a mild integrability condition on the data.

Keywords

Asymptotic Solution, BSDEs, Measure data, Parabolic, Semilinear

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