相关论文: Uniqueness of Weak Solutions to One-Dimensional Do…
In this work, we study the doubly degenerate nutrient taxis system with logistic source \begin{align} \begin{cases}\tag{$\star$}\label{eq 0.1} u_t=\nabla \cdot(u^{l-1} v \nabla u)- \nabla \cdot\left(u^{l} v \nabla v\right)+ u - u^2, \\…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
This paper is devoted to the study of the existence and uniqueness of global admissible conservative weak solutions for the periodic single-cycle pulse equation. We first transform the equation into an equivalent semilinear system by…
By choosing convenient test functions and using the method of doubling variables, we prove the uniqueness of the solution to a nonlinear evolution dam problem in an arbitrary heterogeneous porous medium of IR^n with an impermeable…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the…
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a…
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 prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
We investigated existence of global weak solutions for a system of chemotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of…
Systems of the type $$\begin{cases} u_t = \nabla \cdot (D_1(u) \nabla u - S_1(u) \nabla v) + f_1(u, v),\\ v_t = \nabla \cdot (D_2(v) \nabla v + S_2(v) \nabla u) + f_2(u, v) \end{cases} \qquad (\star)$$ can be used to model pursuit-evasion…
This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to…
The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition…
In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…
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 article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth. The mathematical challenge is due to the fact that the…
We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
This paper is concerned with a strongly degenerate convection-diffusion equation in one space dimension whose convective flux involves a non-linear function of the total mass to one side of the given position. This equation can be…