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Identifier 000439184
Title A stochastic mass conserved reaction-diffusion equation
Alternative Title Στοχαστικές διαφορικές εξισώσεις αντίδρασης-διάχυσης με διατήρηση μάζας
Author Γκικοπούλου, Αφροδίτη
Thesis advisor Καραλή Γεωργία
Reviewer Μακράκης, Γεώργιος
Καμβύσης, Σπυρίδων
Abstract We prove the existence and uniqueness of weak solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of ℝ𝑛 with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion. We decompose our original problem into two problems: a nonlinear stochastic heat equation with homogeneous initial condition, and a stochastic nonlocal reaction diffusion equation with nonlinear reaction but without the noise term. We will prove the existence of solution for these two problems by applying a Galerkin method, which amounts to establishing suitable a priori estimates that we need to get weak compactness of the approximate solution, namely convergence along a subsequence to a limit. The main problem is then to identify the limit of the diffusion term and the reaction term, which we do by means of the so-called monotonicity method. We also prove the uniqueness of the weak solution.
Language English, Greek
Subject Conservation of mass
Nonlinear diffusion
Μη γραμμική διάχυση
Στοχαστική Allen-Cahn εξίσωση
Issue date 2021-03-26
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
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