TY - JOUR
T1 - Decay for nonlinear Klein-Gordon equations
AU - Georgiev, Vladimir
AU - Lucente, Sandra
PY - 2004/12/1
Y1 - 2004/12/1
N2 - We study the asymptotic behavior 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. In these spaces of fractional order we obtain a weighted Sobolev embedding and a nonlinear estimate. Using these, we establish the decay estimate of the solution for large time provided the power of nonlinearity is greater than a critical value.
AB - We study the asymptotic behavior 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. In these spaces of fractional order we obtain a weighted Sobolev embedding and a nonlinear estimate. Using these, we establish the decay estimate of the solution for large time provided the power of nonlinearity is greater than a critical value.
KW - Semilinear Klein-Gordon equation
KW - Weighted Sobolev spaces
UR - http://www.scopus.com/inward/record.url?scp=12744277572&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=12744277572&partnerID=8YFLogxK
U2 - 10.1007/s00030-004-2027-z
DO - 10.1007/s00030-004-2027-z
M3 - Article
AN - SCOPUS:12744277572
SN - 1021-9722
VL - 11
SP - 529
EP - 555
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 4
ER -