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:
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