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June 2015 Decay estimates for solutions of nonlocal semilinear equations
Marco Cappiello, Todor Gramchev, Luigi Rodino
Nagoya Math. J. 218: 175-198 (June 2015). DOI: 10.1215/00277630-2891745


We investigate the decay for |x| of weak Sobolev-type solutions of semilinear nonlocal equations Pu=F(u). We consider the case when P=p(D) is an elliptic Fourier multiplier with polyhomogeneous symbol p(ξ), and we derive algebraic decay estimates in terms of weighted Sobolev norms. Our basic example is the celebrated Benjamin–Ono equation

(0.1)(|D|+c)u=u2,c>0, for internal solitary waves of deep stratified fluids. Their profile presents algebraic decay, in strong contrast with the exponential decay for KdV shallow water waves.


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Marco Cappiello. Todor Gramchev. Luigi Rodino. "Decay estimates for solutions of nonlocal semilinear equations." Nagoya Math. J. 218 175 - 198, June 2015.


Published: June 2015
First available in Project Euclid: 11 May 2015

zbMATH: 1359.35067
MathSciNet: MR3345627
Digital Object Identifier: 10.1215/00277630-2891745

Primary: 35J61
Secondary: 35B40 , 35Q51 , 35S05

Keywords: decay estimates , nonlocal semilinear elliptic equations , solitary waves

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal


Vol.218 • June 2015
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