Flow decomposition for heat equations with memory
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912128852557824 |
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| author | Wang, Gengsheng Zhang, Yubiao Zuazua, Enrique |
| author_facet | Wang, Gengsheng Zhang, Yubiao Zuazua, Enrique |
| contents | We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It consists of three components: The first one is of parabolic nature; the second one gathers the hyperbolic component of the dynamics, with null velocity of propagation; the last one exhibits a finite smoothing effect. This decomposition reveals the hybrid parabolic-hyperbolic nature of the flow and clearly illustrates the significant impact of the memory term on the parabolic behavior of the system in the absence of memory terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_09867 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Flow decomposition for heat equations with memory Wang, Gengsheng Zhang, Yubiao Zuazua, Enrique Analysis of PDEs We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It consists of three components: The first one is of parabolic nature; the second one gathers the hyperbolic component of the dynamics, with null velocity of propagation; the last one exhibits a finite smoothing effect. This decomposition reveals the hybrid parabolic-hyperbolic nature of the flow and clearly illustrates the significant impact of the memory term on the parabolic behavior of the system in the absence of memory terms. |
| title | Flow decomposition for heat equations with memory |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2101.09867 |