Titlebook: Evolution Equations of Hyperbolic and Schrödinger Type; Asymptotics, Estimat Michael Ruzhansky,Mitsuru Sugimoto,Jens Wirth Book 2012 Spring

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Local in Space Energy Estimates for Second-order Hyperbolic Equations,The second part of the paper is devoted to the Cauchy problem for the second-order linear hyperbolic equations. For these equations, we are in the position to get an energy estimate along the cones of determinacy, which will imply, for the corresponding semilinear equations, the analytic propagation

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The Final Problem on the Optimality of the General Theory for Nonlinear Wave Equations,

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Evolution Equations of Hyperbolic and Schrödinger TypeAsymptotics, Estimat

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What Happens in the Start-up Process?,lar, we focus on Schrödinger-type FIOs, showing that Gabor frames provide optimally sparse representations of such operators. Using Maple software, new numerical examples for the Harmonic Oscillator are provided.

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Evolution Equations of Hyperbolic and Schrödinger Type978-3-0348-0454-7Series ISSN 0743-1643 Series E-ISSN 2296-505X

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https://doi.org/10.1007/978-3-319-75907-4cients . are assumed to be bounded and . is assumed to be uniformly elliptic and to coincide with −∆ outside of a ball. A Limiting Absorption Principle (LAP) is proved in the framework of weighted Sobolev spaces. It is then used for (i) A general eigenfunction expansion theorem and (ii) Global space