Results 31 to 40 of about 469 (57)

On Global existence for nonlinear wave equations outside of convex obstacles [PDF]

arXiv, 1999
We prove global existence for semilinear hyperbolic equations that satisfy the null condition of Christodoulou and Klainerman in the exterior of convex domains. We use a combination of the conformal method of Christodoulou and the direct method of Klainerman.
arxiv  

Weighted Strichartz estimates and global existence for semilinear wave equations [PDF]

American Journal of Mathematics, 119 (1997), 1291-1319, 1999
We prove certain weighted Strichartz estimates and use these to prove a sharp theorem for global existence of small amplitude solutions of $\square u= |u|^p$, thus verifying the so-called "Strauss conjecture".
arxiv  

Global Existence for Systems of Nonlinear Wave Equations in 3D with Multiple Speeds [PDF]

arXiv, 2000
Global smooth solutions to the initial value problem for systems of nonlinear wave equations with multiple propagation speeds will be constructed in the case of small initial data and nonlinearities satisfying the null condition.
arxiv  

Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions

Advances in Difference Equations, 2011
A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order
Tatar Nasser-eddine
doaj  

Almost global existence for some semilinear wave equations [PDF]

arXiv, 2001
We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave equations, as opposed to the much harder to prove 1/t decay.
arxiv  

On the continuity of the solution operator to the wave map system [PDF]

Communications on Pure Applied Mathematics, 57(3), 2004, p.357 - 353, 2002
We investigate the continuity properties of the solution operator to the wave map system from the flat Minkowski space to a general nonflat target of arbitrary dimension, and we prove by an explicit class of counterexamples that this map is not uniformly continuous in the critical norms on any neighbourhood of zero.
arxiv  

Local well-posedness for the Maxwell-Schrödinger equation [PDF]

arXiv, 2003
Time local well-posedness for the Maxwell-Schr\"odinger equation in the coulomb gauge is studied in Sobolev spaces by the contraction mapping principle. The Lorentz gauge and the temporal gauge cases are also treated by the gauge transform.
arxiv  

Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping

Boundary Value Problems, 2011
In this paper, we consider the system of nonlinear viscoelastic equations u t t - Δ u + ∫ 0 t g 1 ( t - τ ) Δ u ( τ ) d τ - Δ u t = f 1 ( u , v ) , ( x , t )
Liang Fei, Gao Hongjun
doaj  

On the wave equation with a large rough potential [PDF]

arXiv, 2003
We prove an optimal dispersive $L^{\infty}$ decay estimate for a three dimensional wave equation perturbed with a large non smooth potential belonging to a particular Kato class. The proof is based on a spectral representation of the solution and suitable resolvent estimates for the perturbed operator.
arxiv  

Estimates for the Dirichlet-wave equation and applications to nonlinear wave equations [PDF]

arXiv, 2003
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
arxiv