In this work we study the decay properties of the semilinear Klein-Gordon equation with nonlinearity of fractional order. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid: X = {(t, x) \ t(2) - \x\(2) = 1, t greater than or equal to 1}. In these spaces of fractional order we obtain a weighted Sobolev inequality and a nonlinear estimate. Using these estimates we study the decay property of the solution for large t provided the power of nonlinearity is greater than a critical value. (C) Academie des Sciences/Elsevier, Paris.
Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation / Georgiev V; Lucente S. - In: COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE. - ISSN 0764-4442. - 329:1(1999), pp. 21-26.
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Titolo: | Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation |
Autori: | |
Data di pubblicazione: | 1999 |
Rivista: | |
Citazione: | Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation / Georgiev V; Lucente S. - In: COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE. - ISSN 0764-4442. - 329:1(1999), pp. 21-26. |
Abstract: | In this work we study the decay properties of the semilinear Klein-Gordon equation with nonlinearity of fractional order. By the aid of a suitable generalization of the weighted Sobolev spaces we define the weighted Sobolev spaces on the upper branch of the unit hyperboloid: X = {(t, x) \ t(2) - \x\(2) = 1, t greater than or equal to 1}. In these spaces of fractional order we obtain a weighted Sobolev inequality and a nonlinear estimate. Using these estimates we study the decay property of the solution for large t provided the power of nonlinearity is greater than a critical value. (C) Academie des Sciences/Elsevier, Paris. |
Handle: | http://hdl.handle.net/11586/56667 |
Appare nelle tipologie: | 1.1 Articolo in rivista |