On the -decay and local energy decay of solutions to nonlinear Klein-Gordon equations
Philip Brenner (2003)
Banach Center Publications
Similarity:
Philip Brenner (2003)
Banach Center Publications
Similarity:
Neal Bez, Keith M. Rogers (2013)
Journal of the European Mathematical Society
Similarity:
We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the norm of the solution in terms of the energy. We also characterise the maximisers.
Xu Yin, Waixiang Cao, Zhimin Zhang (2024)
Applications of Mathematics
Similarity:
We present a unified approach to studying the superconvergence property of the spectral volume (SV) method for high-order time-dependent partial differential equations using the local discontinuous Galerkin formulation. We choose the diffusion and third-order wave equations as our models to illustrate approach and the main idea. The SV scheme is designed with control volumes constructed using the Gauss points or Radau points in subintervals of the underlying meshes, which leads to two...
Rémi Carles, David Lannes (2003)
Bulletin de la Société Mathématique de France
Similarity:
We consider a system of two linear conservative wave equations, with a nonlinear coupling, in space dimension three. Spherical pulse like initial data cause focusing at the origin in the limit of short wavelength. Because the equations are conservative, the caustic crossing is not trivial, and we analyze it for particular initial data. It turns out that the phase shift between the incoming wave (before the focus) and the outgoing wave (past the focus) behaves like , where stands for...
Anton Savostianov, Sergey Zelik (2014)
Mathematica Bohemica
Similarity:
We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of with damping terms of the form , where or . The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when . For existence of smooth attractors is more complicated...
Brandner, Marek, Míka, Stanislav
Similarity:
In this paper we study conservation laws with spatially-varying flux functions. We give a survey of some schemes (based on finite volume methods) to solve non-autonomous conservation laws of the form . Numerical experiments are presented.
Abdulatif Badenjki, Gerald G. Warnecke (2019)
Applications of Mathematics
Similarity:
We give a proof of the existence of a solution of reconstruction operators used in the DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect...
Thomas Duyckaerts, Carlos E. Kenig, Frank Merle (2011)
Journal of the European Mathematical Society
Similarity:
Consider the energy-critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, under an appropriate smallness assumption, any type II blow-up radial solution is essentially...
Jonathan Luk (2013)
Journal of the European Mathematical Society
Similarity:
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region .
Martin Del Hierro (2005)
Studia Mathematica
Similarity:
Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in [1], to H-type groups. On those groups we get optimal time decay for solutions to the wave equation (decay as ) and the Schrödinger equation (decay as ), p being the dimension of the center of the group. As a corollary, we obtain the corresponding Strichartz inequalities for the wave equation, and, assuming that p > 1, for the Schrödinger equation.
Nalini Anantharaman, Matthieu Léautaud (2012)
Journées Équations aux dérivées partielles
Similarity:
This article is a proceedings version of the ongoing work [