相关论文: Mathematical analysis of a marine ecosystem model …

We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…

This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of…

Marine ecosystem models are developed to understand and simulate the biogeochemical processes involved in marine ecosystems. Parekh, Follows and Boyle introduced the $PO_4$-$DOP$-$Fe$ model of the coupled phosphorus and iron cycles in 2005.…

We analyse a model of the phosphorus cycle in the ocean given by Slomp and Van Cappellen (2007, https://doi.org/10.5194/bg-4-155-2007). This model contains four distinct oceanic basins and includes relevant parts of the water, carbon and…

We analyze the mathematical properties of a multi-species biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet-Neumann boundary conditions on a bounded domain. This model belongs to the class of…

This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…

We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…

We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this model admits a unique solution under weak conditions on the…

The incompressible Navier-Stokes equations coupled to the Maxwell-Stefan relations for the molar fluxes are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture…

We consider an initial and boundary value problem invoked from the mathematical model for moisture transport in porous materials. Because of the difficulty appearing in the boundary condition, we have changed it and obtain the nonlinear…

We investigate linear parabolic equations in divergence form with singular coefficients and non-smooth boundary data. When the diffusion, drift, or potential terms, as well as the initial or boundary conditions, are distributions rather…

In the present article, we are interested in an initial boundary value problem for a coupled system of partial differential equations arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel.…

This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…

We consider a model system consisting of two reaction-diffusion equations, where one species diffuses in a volume while the other species diffuses on the surface which surrounds the volume. The two equations are coupled via a nonlinear…

In this work, we study the mathematical analysis of a coupled system of two reaction-diffusion-advection equations and Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias) and a…

We study the Landau-Lifshitz system associated with Maxwell equations in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present in the spacer in-between the layers. In the presence of these…

We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…

Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to specific molecules. The corresponding boundary conditions,…

This paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq-Abbott system in the presence of…

We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…