 A qualitative analysis and numerical simulations of a nonlinear second-order anisotropic diffusion problem with non-homogeneous Cauchy–Neumann boundary conditionsTudor Barbu, Alain Miranville and Costică Moroşanu Applied Mathematics and Computation, 2019, vol. 350, issue C, 170-180 Abstract: The paper is concerned with a qualitative analysis for a nonlinear second-order parabolic problem, subject to non-homogeneous Cauchy–Neumann boundary conditions, extending the types already studied. Under some certain assumptions, we prove the existence, estimate, regularity and uniqueness of a classical solution. The considered nonlinear second-order anisotropic diffusion model is then particularized for an image restoration task. The resulted PDE-based model is solved numerically by constructing a finite-difference based approximation algorithm that is consistent to the model and converges fast to its solution. An effective detail-preserving image filtering scheme that removes successfully the white additive Gaussian noise while overcoming the unintended effects is thus obtained. Our successful image restoration and method comparison results are also discussed in this paper. Keywords: Nonlinear anisotropic diffusion; Qualitative properties of solutions; Leray–Schauder principle; Image restoration; Finite difference method; Numerical approximation scheme (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:350:y:2019:i:c:p:170-180 DOI: 10.1016/j.amc.2019.01.004 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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