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On the regularity of solutions of hyperbolic nonlinear equations
Annali di Matematica Pura ed Applicata, 1973Some 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, 2007In 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.
1980Abstract : 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, 1995Nonlinear 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
1995Universal 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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The nonlinear Schrödinger equation on the hyperbolic space
200432 pages, final preprint ...
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