Abstract integrodifferential equations and applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915786309763072 |
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| author | de Andrade, Bruno de Santana, Marcos Gabriel |
| author_facet | de Andrade, Bruno de Santana, Marcos Gabriel |
| contents | In this work, we study the initial value problem associated with an abstract integrodifferential equation in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and a blow-up alternative for regular mild solutions to the problem. Additionally, we apply this theory to the Navier-Stokes equations with hereditary viscosity, taking initial data in the scale of fractional power spaces associated with the Stokes operator. We also explore reaction-diffusion problems with memory, considering the effects of super-linear and gradient-type nonlinearities, and initial data in Lebesgue and Besov spaces, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08691 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Abstract integrodifferential equations and applications de Andrade, Bruno de Santana, Marcos Gabriel Analysis of PDEs In this work, we study the initial value problem associated with an abstract integrodifferential equation in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and a blow-up alternative for regular mild solutions to the problem. Additionally, we apply this theory to the Navier-Stokes equations with hereditary viscosity, taking initial data in the scale of fractional power spaces associated with the Stokes operator. We also explore reaction-diffusion problems with memory, considering the effects of super-linear and gradient-type nonlinearities, and initial data in Lebesgue and Besov spaces, respectively. |
| title | Abstract integrodifferential equations and applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.08691 |