Related papers: On a two-species cross attraction system in higher…
We study a two-dimensional quaternary inhibitory system. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited…
Considering a system of equations modeling the chevron pattern dynamics, we show that the corresponding initial boundary value problem has a unique weak solution that continuously depends on initial data, and the semigroup generated by this…
In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the…
We consider the two dimensional Schr\"odinger equation with time dependent delta potential, which represents a model for the dynamics of a quantum particle subject to a point interaction whose strength varies in time. First, we prove global…
The critical dynamics of Model H with a conserved order parameter coupled to a transverse momentum density which describes the gas-liquid or binary-fluid transitions is investigated within the functional renormalization group approach…
The current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains. We first prove the global existence and boundedness of…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We consider a Keller-Segel model with non-linear porous medium type diffusion and nonlocal attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…
We establish an existence theorem for the doubly periodic vortices in a generalized self-dual Chern--Simons model. We show that there exists a critical value of the coupling parameter such that there exits self-dual doubly periodic vortex…
We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder and chain type defects, non-universal…
In this paper we derive a new model for visco-elasticity with large deformations where the independent variables are the stretch and the rotation tensors which intervene with second gradients terms accounting for physical properties in the…
Isotropic pair potentials that are bounded at the origin have been proposed from time to time as models of the effective interaction between macromolecules of interest in the chemical physics of soft matter. We present a thorough study of…
We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved…
We consider a vertex model in d dimensions characterized by lines which run in a preferred direction. We show that this vertex model is soluble if the weights of vertices with intersecting lines are given by a free-fermion condition, and…
We consider a Keller-Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…
This paper concerns the asymptotics of certain parabolic-elliptic chemotaxis-consumption systems with logistic growth and constant concentration of chemoattractant on the boundary. First we prove that in two dimensional bounded domains…
We study a nonlinear system coupling the Darcy-Forchheimer-Brinkman equations with a convection-diffusion-reaction equation, arising in reactive transport through porous media. The model features a nonlinear viscosity coupling, Forchheimer…
The first massive level of closed bosonic string theory is studied. Free-field equations are derived by imposing Weyl invariance on the world sheet. A two-parameter solution to the equation of motion and constraints is found in two…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…
We prove the existence of a compact global attractor for the dynamics of the forced critical surface quasi-geostrophic equation (SQG) and prove that it has finite fractal (box-counting) dimension. In order to do so we give a new proof of…