New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation
In this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=0,β≠0 is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σt∼t−1/2 for the uniform radius o...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/ijde/2947966 |
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| author | Tegegne Getachew |
| author_facet | Tegegne Getachew |
| author_sort | Tegegne Getachew |
| collection | DOAJ |
| description | In this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=0,β≠0 is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σt∼t−1/2 for the uniform radius of spatial analyticity of solutions to the Kawahara equation. This improves a recent result due to Ahn et al.’s study, where they demonstrated a decay rate of order t−1. Our strategy mainly relies on an approximate conservation law in a modified Gevrey space and bilinear estimate in Bourgain space. |
| format | Article |
| id | doaj-art-b144e40daaf94c3786edea7df6431499 |
| institution | DOAJ |
| issn | 1687-9651 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-b144e40daaf94c3786edea7df64314992025-08-20T03:12:39ZengWileyInternational Journal of Differential Equations1687-96512025-01-01202510.1155/ijde/2947966New Lower Bounds of Spatial Analyticity Radius for the Kawahara EquationTegegne Getachew0Department of MathematicsIn this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=0,β≠0 is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σt∼t−1/2 for the uniform radius of spatial analyticity of solutions to the Kawahara equation. This improves a recent result due to Ahn et al.’s study, where they demonstrated a decay rate of order t−1. Our strategy mainly relies on an approximate conservation law in a modified Gevrey space and bilinear estimate in Bourgain space.http://dx.doi.org/10.1155/ijde/2947966 |
| spellingShingle | Tegegne Getachew New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation International Journal of Differential Equations |
| title | New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation |
| title_full | New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation |
| title_fullStr | New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation |
| title_full_unstemmed | New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation |
| title_short | New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation |
| title_sort | new lower bounds of spatial analyticity radius for the kawahara equation |
| url | http://dx.doi.org/10.1155/ijde/2947966 |
| work_keys_str_mv | AT tegegnegetachew newlowerboundsofspatialanalyticityradiusforthekawaharaequation |