On a nonhomogeneous heat equation on the complex plane
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916325298798592 |
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| author | Son, Duong Ngoc Van Thuy, Tran Xuan, Pham Truong |
| author_facet | Son, Duong Ngoc Van Thuy, Tran Xuan, Pham Truong |
| contents | In this article, we investigate the existence, uniqueness, and asymptotic behaviors of mild solutions of a parabolic evolution equations on complex plane, in which the diffusion operator has the form \(\overline{\Box}_φ = \overline{D}\, \overline{D}^{\ast}\), where \(\overline{D} f = \bar{\partial}f + φ_{\bar{z}} f\), the function \(φ\) is smooth and subharmonic on \(\mathbb{C}\), and \(\overline{D}^{\ast}\) is the formal adjoint of \(\overline{D}\). Our method combines certain estimates of heat kernel associating with the homogeneous linear equation of Raich \cite{raich06} and a fixed point argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a nonhomogeneous heat equation on the complex plane Son, Duong Ngoc Van Thuy, Tran Xuan, Pham Truong Analysis of PDEs Complex Variables In this article, we investigate the existence, uniqueness, and asymptotic behaviors of mild solutions of a parabolic evolution equations on complex plane, in which the diffusion operator has the form \(\overline{\Box}_φ = \overline{D}\, \overline{D}^{\ast}\), where \(\overline{D} f = \bar{\partial}f + φ_{\bar{z}} f\), the function \(φ\) is smooth and subharmonic on \(\mathbb{C}\), and \(\overline{D}^{\ast}\) is the formal adjoint of \(\overline{D}\). Our method combines certain estimates of heat kernel associating with the homogeneous linear equation of Raich \cite{raich06} and a fixed point argument. |
| title | On a nonhomogeneous heat equation on the complex plane |
| topic | Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2406.06895 |