Related papers: A strongly degenerate parabolic aggregation equati…
We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric singular kernel. We define a notion of weak solution adapted to…
This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…
This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. It has previously been shown that if the random…
A class of linear degenerate elliptic equations inspired by nonlinear diffusions of image processing is considered. It is characterized by an interior degeneration of the diffusion coefficient. It is shown that no particularly natural,…
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and…
In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to…
It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We propose a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to…
In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…
We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation may admit a type change ranging from parabolic to elliptic…
We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…
This article is concerned with the development of a theoretical framework of global measure-valued solutions for a class of hyperbolic-parabolic cross-diffusion systems, and its application to the convergence analysis of a fully discrete…
In this work, we study a system of degenerate parabolic equations modeling the dynamics of multiple cell populations in intestinal crypts. The model describes cell division, differentiation, and migration through a strongly coupled system…
In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent…
In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant…
We investigate a two-scale system featuring an upscaled parabolic dispersion-reaction equation intimately linked to a family of elliptic cell problems. The system is strongly coupled through a dispersion tensor, which depends on the…
A general high-order fully explicit scheme based on projective integration methods is here presented to solve systems of degenerate parabolic equations in general dimensions. The method is based on a BGK approximation of the…
This paper is devoted to the analysis of non-negative solutions for a generalisation of the parabolic equation with porous medium like nonlinear diffusion and nonlinear nonlocal reaction. We investigate under which conditions equilibration…
We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a fully…