WELL-POSEDNESS AND NUMERICAL SIMULATIONS OF AN ANISOTROPIC REACTION-DIFFUSION MODEL IN CASE 2D
Anca Croitoru, Costică Moroşanu, Gabriela Tănase
Abstract
<abstract> This paper presents a qualitative study of a nonlinear second-order parabolic problem, endowed with a nonlinearity of cubic type as well as non-homogeneous Cauchy-Neumann boundary conditions. Under certain hypotheses on the input data ($ f(t,x), w(t,x), v_0(x) $), we prove the well-posedness and a priori estimates of a solution in the Sobolev space $ W^{1,2}_p(Q) $, extending the results already proven by other authors. Our mathematical model can be applied in many physical phenomena, such as image processing. Numerical simulations illustrate the effectiveness of the mathematical model in image restoration. </abstract>
Topics & Concepts
Sobolev spaceMathematicsA priori and a posterioriMathematical analysisNonlinear systemHomogeneousReaction–diffusion systemBoundary value problemCauchy distributionApplied mathematicsCauchy problemNeumann boundary conditionAnisotropic diffusionAnisotropyInitial value problemPhysicsCombinatoricsQuantum mechanicsPhilosophyEpistemologyAdvanced Mathematical Physics ProblemsNumerical methods in inverse problemsAdvanced Mathematical Modeling in Engineering