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Scattering for Semilinear Wave Equations with Small Data in Three Space Dimensions.

Hartmut Pecher (1988)

Mathematische Zeitschrift

Selfsimilar profiles in large time asymptotics of solutions to damped wave equations

Grzegorz Karch (2000)

Studia Mathematica

Large time behavior of solutions to the generalized damped wave equation $u_{t t} + A u_{t} + ν B u + F (x, t, u, u_{t}, \nabla u) = 0$ for $(x, t) \in ℝ^{n} \times [0, \infty)$ is studied. First, we consider the linear nonhomogeneous equation, i.e. with F = F(x,t) independent of u. We impose conditions on the operators A and B, on F, as well as on the initial data which lead to the selfsimilar large time asymptotics of solutions. Next, this abstract result is applied to the equation where $A u_{t} = u_{t}$ , $B u = - Δ u$ , and the nonlinear term is either $| u_{t} |^{q - 1} u_{t}$ or ${| u |}^{α - 1} u$ . In this case, the asymptotic profile of solutions is given...

Semidiscrete and single step fully discrete approximations for second order hyperbolic equations

Garth A. Baker, James H. Bramble (1979)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Semidiscrete and single step fully discrete finite element approximations for second order hyperbolic equations with nonsmooth solutions

L. A. Bales (1993)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Semilinear wave equation on manifolds

F. D. Araruna, G. O. Antunes, L. A. Medeiros (2002)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Small solutions to semi-linear wave equations with radial data of critical regularity.

K. Hidano (2009)

Revista Matemática Iberoamericana

Solution explicite du problème de Cauchy pour un opérateur hyperbolique à caractéristiques non régulières

S. Alinhac (1976/1977)

Séminaire Équations aux dérivées partielles (Polytechnique)

Solution globale de l'équation d'un gaz visqueux isotherme dans l'espace entier avec une grande force extérieure dérivant d'un potentiel

Rachid Benabidallah (1995)

Rendiconti del Seminario Matematico della Università di Padova

Solutions $C^{\infty}$ d’une classe de problèmes de Cauchy quasi-linéaires hyperboliques du second ordre sur un conoïde caractéristique

Marcel Dossa (2002)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Solutions globales des systèmes de Dirac-Klein-Gordon

Alain Bachelot (1987)

Journées équations aux dérivées partielles

Solutions of abstract hyperbolic equations by Rothe method.

Milan Pultar (1984)

Aplikace matematiky

Some examples of hyperbolic equations without local solvability

F. Colombini, S. Spagnolo (1989)

Annales scientifiques de l'École Normale Supérieure

Some isometrical identities in the wave equation.

Saitoh, Saburou (1984)

International Journal of Mathematics and Mathematical Sciences

Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method

Abdallah Bradji, Jürgen Fuhrmann (2014)

Mathematica Bohemica

We consider a family of conforming finite element schemes with piecewise polynomial space of degree $k$ in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is $h^{k} + τ^{2}$ in the discrete norms of $ℒ^{\infty} (0, T; ℋ^{1} (Ω))$ and $𝒲^{1, \infty} (0, T; ℒ^{2} (Ω))$ , where $h$ and $τ$ are the mesh size of the spatial and temporal discretization, respectively....

Currently displaying 1 – 20 of 21