相关论文: Unveiling Explicit Patterns: Exact Steady States a…

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic Ginzburg-Landau equation) we observe a discrete family of soliton pairs with…

This paper deals with the Keller--Segel system with signal-dependent sensitivity \begin{equation*} u_t=\Delta u - \nabla \cdot (u \chi(v)\nabla v), \quad v_t=\Delta v + u - v, \quad x\in\Omega,\ t>0, \end{equation*} where $\Omega$ is a…

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…

This paper is concerned with numerical approximation of some two-dimensional Keller-Segel chemotaxis models, especially those generating pattern formations. The numerical resolution of such nonlinear parabolic-parabolic or…

We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique…

We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…

The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem…

Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative…

We investigate a model for pattern formation in the presence of Galilean symmetry proposed by Matthews and Cox [Phys.\ Rev.\ E \textbf{62}, R1473 (2000)], which has the form of coupled generalized Burgers and Ginzburg-Landau-type equations.…

We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…

This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of…

We show that bounded cohomology stabilizes along sequences of classical Lie groups, and along sequences of lattices in them. Our method is based on a criterion from (arXiv:2307.12808) which adapts Quillen's stability method to the setting…

The Cauchy problem in $\mathbb R^n$ is considered for \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v),\\ 0 = \Delta v + u. \end{array} \right. \end{eqnarray*} For each $n\ge 10$, a statement on stability…

Two new families of self-consistent axisymmetric truncated equilibrium models for the description of quasi-relaxed rotating stellar systems are presented. The first extends the spherical King models to the case of solid-body rotation. The…

In the current paper, we study stability, bifurcation, and spikes of positive stationary solutions of the following parabolic-elliptic chemotaxis system with singular sensitivity and logistic source, \begin{cases} u_t=u_{xx}-\chi…

Modeling microstructural evolution at large strains requires mechanical formulations that remain thermodynamically consistent while capturing significant lattice rotations and transformation-induced stresses. However, most existing…

We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study…

We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…