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Renormalized Entropy Solutions for Quasi-linear Anisotropic Degenerate Parabolic Equations
TLDR
We prove the well posedness (existence and uniqueness) of renormalized entropy solutions to the Cauchy problem for quasilinear anisotropic degenerate parabolic equations with L data. Expand
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Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
TLDR
We prove well-posedness (existence and uniqueness) results for a class of degenerate reaction-diffusion systems for the bidomain model. Expand
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Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropyExpand
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Renormalized solutions for a nonlinear parabolic equation with variable exponents and l(1)-data
Abstract We prove the well-posedness (existence and uniqueness) of a renormalized solution to nonlinear parabolic equations with variable exponents and L 1 -data. The functional setting involvesExpand
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A reaction–diffusion system modeling predator–prey with prey-taxis
We are concerned with a system of nonlinear partial differential equations modeling the Lotka–Volterra interactions of predators and preys in the presence of prey-taxis and spatial diffusion. TheExpand
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On 3D DDFV Discretization of Gradient and Divergence Operators: Discrete Functional Analysis Tools and Applications to Degenerate Parabolic Problems
TLDR
We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete W1,p compactness, discrete compactness in space and in time) for the so-called Discrete Duality Finite Volume schemes in three space dimensions. Expand
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Conservative cross diffusions and pattern formation through relaxation
Abstract This paper is aimed at studying the formation of patches in a cross-diffusion system without reaction terms when the diffusion matrix can be negative but with positive self-diffusion. WeExpand
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Finite volume methods for degenerate chemotaxis model
TLDR
A finite volume method for solving the degenerate chemotaxis model is presented, along with numerical examples. Expand
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On some anisotropic reaction-diffusion systems with L1-data modeling the propagation of an epidemic disease
In this paper, we prove the existence of weak solutions for a reaction-di"usion system with general anisotropic di"usivities and transport e"ects, supplemented with either mixed boundary conditionsExpand
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Adaptive multiresolution schemes with local time stepping for two-dimensional degenerate reaction--diffusion systems
Spatially two-dimensional, possibly degenerate reaction-diffusion systems, with a focus on models of combustion, pattern formation and chemotaxis, are solved by a fully adaptive multiresolutionExpand
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