Related papers: Pattern formation in nonlocal Kondo model
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in $\mathbb R^2$. This solves an open problem. We introduce a new methodology of transforming the single nonlocal…
We show that a Kondo-type model with an orbital degeneracy has a new non-Fermi-liquid fixed point. Near the fixed point the spin degrees of freedom are completely quenched, and the residual charge degrees of freedom lead to the…
A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…
We show a stochastic version of the Schauder-Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction-diffusion equations driven by a cylindrical Wiener process and a…
We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-posedness and write the solution explicitly, via some…
We present new local and global dynamic bifurcation results for nonlinear evolution equations of the form $u_t+A u=f_\lambda(u)$ on a Banach space $X$, where $A$ is a sectorial operator, and $\lambda\in R$ is the bifurcation parameter.…
We study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \[ u_t = D u_{xx} + u(1-\phi*u), \] where $\phi*u$ is a spatial convolution with the top hat kernel, $\phi(y) \equiv…
In this paper we investigate pattern formation in Keller--Segel chemotaxis models over a multi--dimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its…
We investigate fractional Cauchy type problem. By using Schauder fixed point theorem we obtain sufficient conditions for the global attractivity of solutions for nonlinear fractional differential equations in weighted spaces.
The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant…
This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near…
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction…
We introduce a delay nonlinear differential equation model which describes how fish are harvested. In our previous studies we investigated the persistence of that equation and existence of a periodic solution for this equation. Here we…
Semidiscretization in time is studied for a class of quasi-linear evolution equations in a framework due to Kato, which applies to symmetric first-order hyperbolic systems and to a variety of fluid and wave equations. In the regime where…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
Understanding the nature of local-itinerant transition of strongly correlated electrons is one of the central problems in condensed matter physics. Heavy fermion systems describe the f-electron delocalization through Kondo interactions with…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…