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On the regularity of solutions of hyperbolic nonlinear equations

Annali di Matematica Pura ed Applicata, 1973
Some regularity results for the solutions of certain hyperbolic nonlinear equations are given.
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The Nonlinear Schrödinger Equation on Hyperbolic Space

Communications in Partial Differential Equations, 2007
In this article we study some aspects of dispersive and concentration phenomena for the Schrodinger equation posed on hyperbolic space  n , in order to see if the negative curvature of the manifold gets the dynamics more stable than in the Euclidean case.
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A Nonlinear Hyperbolic Volterra Equation in Viscoelasticity.

1980
Abstract : A general model for the nonlinear motion of a one dimensional, finite, homogeneous, viscoelastic body is developed and analysed by an energy method. It is shown that under physically reasonable conditions the nonlinear boundary, initial value problem has a unique, smooth solution (global in time), provided the given data are sufficiently ...
J. A. Nohel, C. M. Dafermos
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Nonlinear hyperbolic differential equations in microelectronics

Korean Journal of Computational & Applied Mathematics, 1995
Nonlinear hyperbolic differential equations have been a subject of intense research in the field of gas dynamics due to many engineering problems associated with high-speed airplanes, missiles, materials processing, etc. Recently, phenomena known from gas dynamics are found to occur also in the microeletronic devices such as MOSFET.
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Asymptotic Equations for Nonlinear Hyperbolic Waves

1995
Universal asymptotic equations. It is a remarkable fact that, in suitable asymptotic limits, the behavior of almost all nonlinear waves is described by a few rather simple looking nonlinear equations. Examples include Burgers equation, the Kortewegde Vries (KdV) equation, and the nonlinear Schrodinger equation.
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