An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915492831166464 |
|---|---|
| author | Choi, Jae-Hwan Kim, Ildoo |
| author_facet | Choi, Jae-Hwan Kim, Ildoo |
| contents | We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This formulation is applicable to evolution equations involving pseudo-differential operators, even when the signs of their symbols may vary over time. Notably, our main operator includes the logarithmic Laplacian operator $\log (-Δ)$ and a second-order differential operator whose leading coefficients are not positive semi-definite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19968 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity Choi, Jae-Hwan Kim, Ildoo Analysis of PDEs Classical Analysis and ODEs 35S05, 35S10, 35A01, 35D30, 47G30 We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This formulation is applicable to evolution equations involving pseudo-differential operators, even when the signs of their symbols may vary over time. Notably, our main operator includes the logarithmic Laplacian operator $\log (-Δ)$ and a second-order differential operator whose leading coefficients are not positive semi-definite. |
| title | An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity |
| topic | Analysis of PDEs Classical Analysis and ODEs 35S05, 35S10, 35A01, 35D30, 47G30 |
| url | https://arxiv.org/abs/2403.19968 |