A time-fractional Fisher-KPP equation for tumor growth: Analysis and numerical simulation
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arXiv
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| Format: | Preprint |
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2025
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| author | Fritz, Marvin Kavallaris, Nikos I. |
| author_facet | Fritz, Marvin Kavallaris, Nikos I. |
| contents | We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive population dynamics and serves as a framework for tumor growth modeling. We first establish local well-posedness of weak solutions. The analysis combines a Galerkin approximation with a refined a priori estimate based on a Bihari-Henry-Gronwall inequality, addressing the nonlinear coupling between the fractional diffusion and the reaction term. For small initial data, we further prove global well-posedness and asymptotic stability. A numerical method based on a nonuniform convolution quadrature scheme is then proposed and validated. Simulations demonstrate distinct dynamical behaviors compared to conventional formulations, emphasizing the physical consistency of the present model in describing tumor progression. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A time-fractional Fisher-KPP equation for tumor growth: Analysis and numerical simulation Fritz, Marvin Kavallaris, Nikos I. Analysis of PDEs Numerical Analysis 35A01, 35R11, 65M12, 65M60, 92C50 We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive population dynamics and serves as a framework for tumor growth modeling. We first establish local well-posedness of weak solutions. The analysis combines a Galerkin approximation with a refined a priori estimate based on a Bihari-Henry-Gronwall inequality, addressing the nonlinear coupling between the fractional diffusion and the reaction term. For small initial data, we further prove global well-posedness and asymptotic stability. A numerical method based on a nonuniform convolution quadrature scheme is then proposed and validated. Simulations demonstrate distinct dynamical behaviors compared to conventional formulations, emphasizing the physical consistency of the present model in describing tumor progression. |
| title | A time-fractional Fisher-KPP equation for tumor growth: Analysis and numerical simulation |
| topic | Analysis of PDEs Numerical Analysis 35A01, 35R11, 65M12, 65M60, 92C50 |
| url | https://arxiv.org/abs/2511.05312 |