Related papers: Generalized Landau-Lifshitz models on the interval
We study local regularity properties of local minimizer of scalar integral functionals of the form $$\mathcal F[u]:=\int_\Omega F(\nabla u)-f u\,dx$$ where the convex integrand $F$ satisfies controlled $(p,q)$-growth conditions. We…
Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic…
The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization dynamics in the presence of an applied field and a spin polarized current. In the case of axial symmetry and with focus on one space dimension, we investigate the…
In our work we study non-variational, nonlinear singularly perturbed elliptic models enjoying a double degeneracy character with prescribed boundary value in a domain. In such a scenario, we establish the existence of solutions. We also…
A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic…
The purpose of this article is to prove existence, uniqueness and uniform gradient estimates for unbounded classical solutions of a Hamilton-Jacobi-Bellman equation. Such an equation naturally arises in stochastic control problems. Contrary…
We consider autonomous and non-autonomous evolution equations on a time interval $[0,\tau]$ in a Banach space $X$ with the non-standard time-boundary condition $u(0)=\Phi u(\tau)$, where $\Phi$ is a linear map on $X$. If $\Phi=0$, this is…
We discuss the initial value problem for the Einstein equations in Hitchin's generalised geometry for the case of closed divergence (which correspond to the equations of motion in the bosonic part of the NS-NS sector in type II…
We consider a port-Hamiltonian system on a spatial domain $\Omega \subseteq \mathbb{R}^n$ that is bounded with Lipschitz boundary. We show that there is a boundary triple associated to this system. Hence, we can characterize all boundary…
Generic classically integrable boundary conditions for the $A_{n}^{(1)}$ affine Toda field theories (ATFT) are investigated. The present analysis rests primarily on the underlying algebra, defined by the classical version of the reflection…
We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to…
After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…
This work proposes an interval observer design for nonlinear discrete-time systems based on the Kazantzis-Kravaris/Luenberger (KKL) paradigm. Our design extends to generic nonlinear systems without any assumption on the structure of its…
We establish the Lipschitz regularity of the a priori bounded local minimizers of integral functionals with non autonomous energy densities satisfying non standard growth conditions under a sharp bound on the gap between the growth and the…
We show that every irreducible representation in the discrete automorphic spectrum of GL(n) admits a non vanishing mixed (Whittaker-symplectic) period integral. The analog local problem is a study of models first considered by Klyachko over…
We consider a class of nonlocal Cahn-Hilliard equations in a bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, subject to a nonlocal kinetic rate dependent dynamic boundary condition. This diffuse interface model describes phase…
We propose new semi-implicit numerical methods for the integration of the stochastic Landau-Lifshitz equation with built-in angular momentum conservation. The performance of the proposed integrators is tested on the 1D Heisenberg chain. For…
A Landau-Lifshitz-Gilbert type equation has been derived by using s-d model in which the s-electron system is regarded as an environment coupled weakly with the localized spins. Based on the irreducible linear response theory, we show that…
We consider the discrete defocusing nonlinear Schr\"odinger equation in its integrable version, which is called defocusing Ablowitz-Ladik lattice. We consider periodic boundary conditions with period $N$ and initial data sample according to…
In this paper, we are concerned with complex Ginzburg-Landau (CGL) equations. There are several results on the global existence and smoothing effects of solutions to the initial boundary value problem for (CGL) in bounded or unbounded…