A Fisher-type evolution equation with applications in image processing
Copyright policy )A Fisher-type evolution equation with applications in image processing
The aim of this paper is to present some applications of the Neumann Laplacian in image processing, along with the necessary mathematical background. We prove weak and strong versions of the maximum principle for weak solutions of elliptic and parabolic problems and apply them to a Fisher K.P.P.-type equation. The original contribution lies in the application of this equation in image processing, where various diffusion-like effects can be achieved. Additionally, a review of the basics of linear and nonlinear PDEs with Neumann boundary conditions is provided, along with updated bibliography and recent qualitative results. There are also some new theoretical results developed in this work.
Semilinear elliptic equations, Neumann Laplacian, weak formulation of PDEs, Asymptotic behavior of solutions to PDEs, asymptotic behaviour, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, strong maximum principle, Computing methodologies for image processing, Maximum principles in context of PDEs, semilinear elliptic and parabolic problems, PDEs in image processing, Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Weak solutions to PDEs, Semilinear parabolic equations
Semilinear elliptic equations, Neumann Laplacian, weak formulation of PDEs, Asymptotic behavior of solutions to PDEs, asymptotic behaviour, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, strong maximum principle, Computing methodologies for image processing, Maximum principles in context of PDEs, semilinear elliptic and parabolic problems, PDEs in image processing, Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Weak solutions to PDEs, Semilinear parabolic equations
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