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

LUCENTE, SANDRA
1999-01-01

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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/56667
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 15
social impact