相关论文: Stationary states of reaction-diffusion and Schr\"…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper has treated the repulsive…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
This paper investigates the global well-posedness of a class of reaction-advection-diffusion models with nonlinear diffusion and Lotka-Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the…
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically…
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only destabilizes constant steady states but also induces blow-up of…
In this paper we study the local instability to the boundary equilibria and the local stability to the positive equilibria for some chemical reaction-diffusion systems. We first analyze a three-species system with boundary equilibria in…
This paper explains the uniqueness of positive steady state of general Lotka-Volterra competition model of two species of animals in the same environment.
This paper studies the Lotka-Volterra competition model with cross-diffusion terms under homogeneous Dirichlet boundary conditions. We consider the asymptotic behavior of positive steady-states as equal two cross-diffusion coefficients tend…
We consider an evolution model with nonlinear diffusion of porous medium type in competition with a nonlocal drift term favoring mass aggregation. The distinguishing trait of the model is the choice of a nonlinear $(s,p)$ Riesz potential…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…