Results 151 to 160 of about 99,243 (193)
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Second Order Hyperbolic Equations with Small Nonlinearities
SIAM Journal on Applied Mathematics, 1978A 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.
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On a Nonlinear Hyperbolic Volterra Equation
SIAM Journal on Mathematical Analysis, 1980We study questions of existence, boundedness and asymptotic behavior of the solutions of the initial value problem \[(*)\qquad \begin{array}{*{20}c} {u_t (t,x) - \int_0^t {a (t - s)\sigma (u_x (s,x))_x = f(t,x),\quad 0 < t < \infty ,\quad x \in R.} } \\ {u(0,x) = u_0 (x),\quad x \in R.} \\ \end{array} \] Here $a:R^ + = [0,\infty ) \to R,\sigma :R \to R,
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On Nonlinear Hyperbolic Functional Differential Equations
Mathematische Nachrichten, 2000The author proves existence of weak solutions of certain second-order evolution equations. The results are applied to higher-order nonlinear hyperbolic functional-differential equations.
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Symmetric hyperbolic equations in the nonlinear elasticity theory
Computational Mathematics and Mathematical Physics, 2008Summary: 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.
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Nonlinear Hyperbolic Equations
1996Here 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.
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Yosida approximation and nonlinear hyperbolic equation
Nonlinear Analysis: Theory, Methods & Applications, 1990We are concerned with the initial value problem for nonlinear evolution equations of the form u″(t)+M(|A 1/2 u(t)| 2 )Au(t)+δu'(t)=f(t) on [0,∞), u(0)=u o , u'(O)=u 1 . Here A is a nonnegative selfadjoint operator in a real Hilbert space H,δ>0 is a constant and M is a C 1 -class function satisfying M(r)≥m o >0 for r≥0, with m o constant.
Ryo Ikehata, Noboru Okazawa
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Nonlinear resonance for quasilinear hyperbolic equation
Journal of Mathematical Physics, 1987The purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source. Resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system. For the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear ...
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Local solutions for a nonlinear degenerate Hyperbolic equation
Nonlinear Analysis: Theory, Methods & Applications, 1986The author investigates local solutions for the initial-boundary value problem associated to the nonlinear degenerated hyperbolic equation of the type \(u_{tt}-M(\int_{\Omega}| \nabla u|^ 2dx)\Delta u=0,\) which comes from the mathematical description of the vibrations of an elastic stretched string.
Ebihara, Y. +2 more
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Cosine Methods for Nonlinear Second-Order Hyperbolic Equations
Mathematics of Computation, 1989We construct and analyze efficient, high-order accurate methods for approximating the smooth solutions of a class of nonlinear, second-order hyperbolic equations. The methods are based on Galerkin type discretizations in space and on a class of fourth-order accurate two-step schemes in time generated by rational approximations to the cosine ...
Bales, Laurence A. +1 more
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A nonlinear hyperbolic volterra equation
1979A 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.
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