Well-posedness of the growth-coagulation equation with singular kernels
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914900673036288 |
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| author | Giri, Ankik Kumar Laurençot, Philippe Si, Saroj |
| author_facet | Giri, Ankik Kumar Laurençot, Philippe Si, Saroj |
| contents | The well-posedness of the growth-coagulation equation is established for coagulation kernels having singularity near the origin and growing atmost linearly at infinity. The existence of weak solutions is shown by means of the method of the characteristics and a weak $L_1$-compactness argument. For the existence result, we also show our gratitude to Banach fixed point theorem and a refined version of the Arzelá-Ascoli theorem. In addition, the continuous dependence of solutions upon the initial data is shown with the help of the DiPerna-Lions theory, Gronwall's inequality and moment estimates. Moreover, the uniqueness of solution follows from the continuous dependence. The results presented in this article extend the contributions made in earlier literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the growth-coagulation equation with singular kernels Giri, Ankik Kumar Laurençot, Philippe Si, Saroj Analysis of PDEs The well-posedness of the growth-coagulation equation is established for coagulation kernels having singularity near the origin and growing atmost linearly at infinity. The existence of weak solutions is shown by means of the method of the characteristics and a weak $L_1$-compactness argument. For the existence result, we also show our gratitude to Banach fixed point theorem and a refined version of the Arzelá-Ascoli theorem. In addition, the continuous dependence of solutions upon the initial data is shown with the help of the DiPerna-Lions theory, Gronwall's inequality and moment estimates. Moreover, the uniqueness of solution follows from the continuous dependence. The results presented in this article extend the contributions made in earlier literature. |
| title | Well-posedness of the growth-coagulation equation with singular kernels |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.02457 |