Invariance properties of the solution operator for measure-valued semilinear transport equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913670882131968 |
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| author | Hille, Sander C. Lyons, Rainey Muntean, Adrian |
| author_facet | Hille, Sander C. Lyons, Rainey Muntean, Adrian |
| contents | We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is preserved, as well as absolute continuity with respect to Lebesgue measure, if the initial condition has that property. Moreover, if the initial condition has $L^p$ regular density, then the solution has the same property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariance properties of the solution operator for measure-valued semilinear transport equations Hille, Sander C. Lyons, Rainey Muntean, Adrian Analysis of PDEs 35Q49 We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is preserved, as well as absolute continuity with respect to Lebesgue measure, if the initial condition has that property. Moreover, if the initial condition has $L^p$ regular density, then the solution has the same property. |
| title | Invariance properties of the solution operator for measure-valued semilinear transport equations |
| topic | Analysis of PDEs 35Q49 |
| url | https://arxiv.org/abs/2501.18026 |