WELL-POSEDNESS AND NUMERICAL SIMULATIONS OF AN ANISOTROPIC REACTION-DIFFUSION MODEL IN CASE 2D

Anca Croitoru; Costică Moroşanu; Gabriela Tănase

doi:10.11948/20200359

2021 Volume 11 Issue 5

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Anca Croitoru, Costică Moroşanu, Gabriela Tănase. WELL-POSEDNESS AND NUMERICAL SIMULATIONS OF AN ANISOTROPIC REACTION-DIFFUSION MODEL IN CASE 2D[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2258-2278. doi: 10.11948/20200359

Citation:

Anca Croitoru, Costică Moroşanu, Gabriela Tănase. WELL-POSEDNESS AND NUMERICAL SIMULATIONS OF AN ANISOTROPIC REACTION-DIFFUSION MODEL IN CASE 2D[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2258-2278. doi: 10.11948/20200359

WELL-POSEDNESS AND NUMERICAL SIMULATIONS OF AN ANISOTROPIC REACTION-DIFFUSION MODEL IN CASE 2D

1.
Department of Mathematics, University of Iasi, bd. Carol I, Iasi, 700506, Romania

Corresponding authors: croitoru@uaic.ro(A. Croitoru); costica.morosanu@uaic.ro (C. Moroşanu); gabriela.tanase@uaic.ro(G. 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.
- Nonlinear anisotropic reaction-diffusion /
- well-posedness of solutions /
- Leray-Schauder principle /
- finite difference method /
- numerical approximation scheme /
- image restoration
MSC: 35Bxx, 35K55, 35K60, 35Qxx, 65Nxx, 68U10

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References

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