Related papers: Christoffel equation in the polarization variables
This paper is concerned with the numerical analysis of linear and nonlinear Schr{\"o}dinger equations with analytic potentials. While the regularity of the potential (and the source term when there is one) automatically conveys to the…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…
We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…
This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…
We study stability of solitary wave solutions for the fractional generalized Korteweg-de Vries equation $$ \partial_t u- \partial_{x_1} D^{\alpha}u+ \tfrac{1}{m}\partial_{x_1}(u^m)=0, ~ (x_1,\dots,x_d)\in \mathbb{R}^d, \, \, t\in…
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…
We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in 2D models of Bose-Einstein condensates with a spatially modulated nonlinearity of either sign and a…
Vortex solutions to the classical field equations in a massive, renormalizable U(1) gauge model are considered in (2+1) dimensions. A vector field whose kinetic term consists of a Chern-Simons term plus a Stuekelberg mass term is coupled to…
We propose to analyse the discretization of the Stokes problem with nonconforming finite elements in light of the T-coercivity (cf. [1] for Helmholtz-like problems, see [2], [3] and [4] for the neutron diffusion equation). We propose…
For arbitrary planar convex domain, we compute the behavior of Christoffel function up to a constant factor using comparison with other simple reference domains. The lower bound is obtained by constructing an appropriate ellipse contained…
We use a change of variables that turns the critical nonlinear Schroedinger equation into the critical nonlinear Schroedinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on…
We consider the semilinear equation $$ \epsilon^{2s} (-\Delta)^s u + V(x)u - u^p = 0, \quad u>0, \quad u\in H^{2s}(\R^N) $$ where $0<s<1,\ 1<p<\frac{N+2s}{N-2s}$, $ V(x)$ is a sufficiently smooth potential with $\inf_\R V(x)> 0$, and…
The Swift-Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift-Hohenberg equation with dispersion are presented. The classification of these solutions is given. It is shown that the Swift-Hohenberg…
This paper studies the stability and large-time behavior of the three-dimensional (3-D) Boltzmann equation near shock profiles. We prove the nonlinear stability of the composite wave consisting of two shock profiles under general…
For the generalized $p$-power Korteweg-de Vries equation, all non-periodic travelling wave solutions with non-zero boundary conditions are explicitly classified for all integer powers $p\geq 1$. These solutions are shown to consist of:…
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial…
We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or…
We study the coalescence of non-spinning binary black holes from near the innermost stable circular orbit down to the final single rotating black hole. We use a technique that combines the full numerical approach to solve Einstein…
In this work, we construct numerical solutions to an inverse problem of a nonlinear Helmholtz equation defined in a spherical shell between two concentric spheres centered at the origin.Assuming that the values of the forward problem are…