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The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
The Landau-Ginzburg-Wilson paradigm is applied to model the low-temperature crystallographic C$\alpha$ backbone structure of sperm whale myoglobin. The Glauber protocol is employed to simulate its response to an increase in ambient…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
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…
This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
In this paper a strongly degenerate parabolic equation derived from a density dependent particle flow model is studied. Furthermore, a free boundary problem and its connection to the strongly degenerate parabolic equation is investigated.…
Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
Discrete Diffusion and Flow Matching models have significantly advanced generative modeling for discrete structures, including graphs. However, the dependencies between intermediate noisy states lead to error accumulation and propagation…
We study an anisotropic, possibly non-homogeneous version of the evolution $p$-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive $L^1$ to…
We show interior H\"older continuity for a class of quasi-linear degenerate reaction-diffusion equations. The diffusion coefficient in the equation has a porous medium type degeneracy and its primitive has a singularity. The reaction term…
Optoacoustic tomography image reconstruction has been a problem of interest in recent years. By exploiting the exceptional generative power of the recently proposed diffusion models we consider a scheme which is based on a conditional…
We show that given an initial vorticity which is bounded and $m$-fold rotationally symmetric for $m \ge 3$, there is a unique global solution to the 2D Euler equation on the whole plane. That is, in the well-known $L^1 \cap L^\infty$ theory…
We present a simple model for the response of a dissipationless spherical system to an instantaneous mass change at its center, describing the formation of flat cores in dark matter haloes and ultra-diffuse galaxies (UDGs) from…
We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…
We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase…
We study a higher-dimensional thin film equation that incorporates competitive effects between aggregation and repulsion, where repulsion is modeled by fourth-order diffusion and aggregation by backward second-order degenerate diffusion,…
We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded…
Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion…