相关论文: Almost sharp nonlinear scattering in one-dimension…
We construct two new classes of spacetimes generated by spinning and traveling magnetic sources in $(n+1)$-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potential. These solutions are neither asymptotically flat nor…
We prove that solutions to linear kinetic equations in a half-space with absorbing boundary conditions decay for large times like $t^{-\frac{1}{2}-\frac{d}{4}}$ in a weighted $\sfL^{2}$ space and like $t^{-1-\frac{d}{2}}$ in a weighted…
We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we prove existence and uniqueness for measure solutions.…
In this paper, we use Dafermos-Rodnianski's new vector field method to study the asymptotic pointwise decay properties for solutions of energy subcritical defocusing semilinear wave equations in $\mathbb{R}^{1+3}$. We prove that the…
In this paper, we consider two types of topological solitons in a generalized Born-Infeld-Higgs model. We explore the self-dual structure of the model and prove the existence of planar vortex solutions. Furthermore, we couple the system…
The Cauchy problem for a quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For some simplified formulation of the problem, a criterion for the…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
A multidimensional cosmological model with scalar and form fields [1-4] is studied. An exact S-brane solution (either electric or magnetic) in a model with l scalar fields and one antisymmetric form of rank m > 1 is considered. This…
We study oscillons in D+1 space-time dimensions using a spherically symmetric ansatz. From Gaussian initial conditions, these evolve by emitting radiation, approaching ``quasi-breathers'', near-periodic solutions to the equations of motion.…
In this paper, we study three-dimensional nonlinear wave equations under the null condition, a fundamental model in the theory of nonlinear wave-type equations, initially investigated by Christodoulou \cite{Christodoulou86} and Klainerman…
In this paper we study a semilinear wave equation with nonlinear, time-dependent damping in one space dimension. For this problem, we prove a well-posedness result in $W^{1,\infty}$ in the space-time domain $(0,1)\times [0,+\infty)$. Then…
We consider {\em discretized} Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular nonlinear part. We consider splitting methods associated with this decomposition. Using a…
The Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave…
We study supersymmetric inhomogeneous field theories in 1+1 dimensions which have explicit coordinate dependence. Although translation symmetry is broken, part of supersymmetries can be maintained. In this paper, we consider the simplest…
This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…
We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains. Our proofs rely on uniform estimates on growing domains, on…
We prove existence and uniqueness of solution of a class of semi-linear wave equations with initial data prescribed on the light-cone with vertex the origin of a Minkowski space-time. The nonlinear term is assumed to satisfy a nullity…
We consider solutions to the initial value problem associated to the intermediate long wave (ILW) equation. We establish persistence properties of the solution flow in weighted Sobolev spaces, and show that they are sharp. We also deal with…
We consider the scalar wave equation with power nonlinearity in n+1 dimensions. Unlike most previous numerical studies, we go beyond the radial case and do not assume any symmetries for n=3, and we only impose an SO(n-1) symmetry in higher…
We investigate the dynamics of roll solutions at the zigzag boundary of the planar Swift-Hohenberg equation. Linear analysis shows an algebraic decay of small perturbation with a $t^{- 1/4}$ rate, instead of the classical $t^{- 1/2}$…