Time decay for nonlinear wave equations in two space dimensions |
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Authors: | Robert Glassey Hartmut Pecher |
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Affiliation: | (1) Department of Mathematics, Indiana University, 47405 Bloomington, IN., USA;(2) Fachbereich Mathematik, Universität Wuppertal, D-5600 Wuppertal 1, Fed. Rep. of Germany |
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Abstract: | The Cauchy Problem for the equation utt–u+|u|p–1u=0 (x2, t>0, >1) is studied. Smooth Cauchy data is prescribed, and no smallness condition is imposed. For >5, it is shown that the maximum amplitude of such a wave decays at the expected rate t–1/2 as t. For 1+8<5, the maximum amplitude still decays, but at a slower rate. These results are then used to demonstrate the existence of the scattering operator when >o, where o is the root of the cubic equation 3-22-7-8=0; thus o4.15.Alfred P. Sloan Research Fellow |
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