Smoothing effect for higher order dispersive equations and applications to nonlinear initial value problems
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| Format: | Preprint |
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2025
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| _version_ | 1866912594756894720 |
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| author | Junior, Alexandre Arias Ascanelli, Alessia Cappiello, Marco |
| author_facet | Junior, Alexandre Arias Ascanelli, Alessia Cappiello, Marco |
| contents | In this paper we deal with the initial value problem related to a family of dispersive inhomogeneous evolution equations Pu=f with variable coefficients belonging to the class of p-evolution equations, $p\geq 2$. We study the smoothing effect produced by some spatial decay assumptions on the imaginary part of the subleading coefficient of the linear operator P. Then we apply this result to nonlinear problems with derivative nonlinearities obtaining existence and uniqueness of the solution in a suitable Sobolev class. The nonlinear equations considered include various equations of physical interest such as KdV-type and Kawahara-type equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_04130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoothing effect for higher order dispersive equations and applications to nonlinear initial value problems Junior, Alexandre Arias Ascanelli, Alessia Cappiello, Marco Analysis of PDEs 35B65, 35G25, 35S05 In this paper we deal with the initial value problem related to a family of dispersive inhomogeneous evolution equations Pu=f with variable coefficients belonging to the class of p-evolution equations, $p\geq 2$. We study the smoothing effect produced by some spatial decay assumptions on the imaginary part of the subleading coefficient of the linear operator P. Then we apply this result to nonlinear problems with derivative nonlinearities obtaining existence and uniqueness of the solution in a suitable Sobolev class. The nonlinear equations considered include various equations of physical interest such as KdV-type and Kawahara-type equations. |
| title | Smoothing effect for higher order dispersive equations and applications to nonlinear initial value problems |
| topic | Analysis of PDEs 35B65, 35G25, 35S05 |
| url | https://arxiv.org/abs/2508.04130 |