Decay estimates for solutions of nonlocal semilinear equations
| Autor: | Todor Gramchev, Luigi Rodino, Marco Cappiello |
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| Rok vydání: | 2015 |
| Předmět: |
General Mathematics
Mathematics::Analysis of PDEs 01 natural sciences Multiplier (Fourier analysis) symbols.namesake Mathematics - Analysis of PDEs Decay estimates Decay estimates nonlocal semilinear elliptic equations solitary waves FOS: Mathematics 35S05 0101 mathematics Exponential decay Algebraic number Korteweg–de Vries equation Mathematics Mathematical physics 35B40 010102 general mathematics 35J61 010101 applied mathematics Sobolev space Waves and shallow water Fourier transform 35Q51 solitary waves symbols nonlocal semilinear elliptic equations Analysis of PDEs (math.AP) |
| Zdroj: | Nagoya Math. J. 218 (2015), 175-198 |
| ISSN: | 2152-6842 0027-7630 |
| Popis: | 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 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. |
| Databáze: | OpenAIRE |
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