Results 271 to 280 of about 10,797 (309)

Second Order Hyperbolic Equations with Small Nonlinearities

SIAM Journal on Applied Mathematics, 1978
A second order partial differential equation which describes the propagation of one-dimensional nonlinear waves in a bounded, inhomogeneous, dissipative medium is analyzed using the method of multiple scales. The conditions under which the oppositely traveling components of the nonlinear motion uncouple to first order are given.
Seymour, Brian R., Mortell, Michael P.
openaire   +2 more sources

On Nonlinear Hyperbolic Functional Differential Equations

Mathematische Nachrichten, 2000
The author proves existence of weak solutions of certain second-order evolution equations. The results are applied to higher-order nonlinear hyperbolic functional-differential equations.
openaire   +2 more sources

A Perturbation Method for Hyperbolic Equations with Small Nonlinearities

SIAM Journal on Applied Mathematics, 1972
A method of multiple scales is developed for the generation of uniformly valid asymptotic solutions of initial value problems for nonlinear wave equations. The method is applicable when the nonlinearities are small and only involve the first derivatives of the dependent variable.
Chikwendu, S. C., Kevorkian, J.
openaire   +2 more sources

Hyperbolicity of the Nonlinear Models of Maxwell?s Equations

Archive for Rational Mechanics and Analysis, 2004
The class of nonlinear models of electromagnetism is considered [see \textit{B. D. Coleman} and \textit{E. H. Dill}, Z. Angew. Math. Phys. 22, 691--702 (1971; Zbl 0218.35072)]. To describe the electromagnetic field \((B,D)\) its energy density \(W(B,D)\) is used. The models are constructed on basis of conservation laws.
openaire   +2 more sources

Symmetric hyperbolic equations in the nonlinear elasticity theory

Computational Mathematics and Mathematical Physics, 2008
Summary: Concerning the formulation of nonlinear elasticity equations in the form of symmetric hyperbolic systems, the article surveys basic results of long-time studies performed under the direction of the first author. The underlying principles developed therein are stated, and some inaccuracies and errors are corrected.
Godunov, S. K., Peshkov, I. M.
openaire   +2 more sources

A family of integrable nonlinear equations of hyperbolic type

Journal of Mathematical Physics, 2001
A new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional reduction of the anti-self-dual Yang–Mills equations, is presented. It represents a generalization of the Ernst–Weyl equation of General Relativity related to colliding neutrino and gravitational waves, as well as of the fourth order equation of Schwarzian ...
Tongas, A., Tsoubelis, D., Xenitidis, P.
openaire   +2 more sources

Solvability of Nonlinear Inverse Problem for Hyperbolic Equation

Journal of Mathematical Sciences, 2017
Summary: We consider the nonlinear inverse problem for a second order hyperbolic equation with unknown coefficient depending on the time. We establish the existence and uniqueness of regular solutions which are used for constructing a solution to the inverse problem under consideration.
openaire   +1 more source

Nonlinear Hyperbolic Equations

1996
Here we study nonlinear hyperbolic equations, with emphasis on quasi-linear systems arising from continuum mechanics, describing such physical phenomena as vibrating strings and membranes and the motion of a compressible fluid, such as air.
openaire   +1 more source

A Branching Random Evolution and a Nonlinear Hyperbolic Equation

SIAM Journal on Applied Mathematics, 1988
The author studies a branching random evolution process as considered by McKean, i.e., a particle moving at constant speed c along the real line, reversing direction as a Poisson process with parameter a, and splitting into \(j\geq 2\) ``daughter'' particles with probability \(b_ j\) \((\sum^{\infty}_{j=2}b_ j=1)\) after a random inter-splitting ...
openaire   +2 more sources

A nonlinear hyperbolic volterra equation

1979
A mathematical model for the motion of a nonlinear one dimensional viscoelastic rod is analysed by an energy method developed by C.M. Dafermos and the author. Global existence, uniqueness, boundedness, and the decay of smooth solutions as t → ∞ are established for sufficiently smooth and "small" data.
openaire   +1 more source