Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1(329), p. 21-26
DOI: 10.1016/s0764-4442(99)80454-6
Full text: Unavailable
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.