Cauchy problem in function spaces with asymptotic expansions with respect to time variable
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913560969347072 |
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| author | Ouchi, Sunao |
| author_facet | Ouchi, Sunao |
| contents | A system of nonlinear Cauchy problem $\partial_t u_i=f_i(t,x, U, \nabla_xU )$ $u_i(0,x)= u_{i,0}(x)$ is studied in function spaces with asymptotic expansion with respect to $t$. To be specific, it is discussed in Borel summable or multisummable function space.It is recognized that these functions are important classes in asymptotic analysis. We study equations under the condition $\{f_i(t,x, U, P)\}_{i=1}^m$ are in these function spaces with respect to $t$ and show $\{u_i(t,x)\}_{i=1}^m$ have also the same summability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cauchy problem in function spaces with asymptotic expansions with respect to time variable Ouchi, Sunao Analysis of PDEs 35F55, Secondary 35A10, 41A60.} A system of nonlinear Cauchy problem $\partial_t u_i=f_i(t,x, U, \nabla_xU )$ $u_i(0,x)= u_{i,0}(x)$ is studied in function spaces with asymptotic expansion with respect to $t$. To be specific, it is discussed in Borel summable or multisummable function space.It is recognized that these functions are important classes in asymptotic analysis. We study equations under the condition $\{f_i(t,x, U, P)\}_{i=1}^m$ are in these function spaces with respect to $t$ and show $\{u_i(t,x)\}_{i=1}^m$ have also the same summability. |
| title | Cauchy problem in function spaces with asymptotic expansions with respect to time variable |
| topic | Analysis of PDEs 35F55, Secondary 35A10, 41A60.} |
| url | https://arxiv.org/abs/2410.17645 |