On a PDE-ODE-PDE model for two interacting cell populations under the influence of an acidic environment and with nonlocal intra- and interspecific growth limitation
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| Format: | Preprint |
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2024
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| _version_ | 1866914128558292992 |
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| author | Eckardt, Maria Surulescu, Christina |
| author_facet | Eckardt, Maria Surulescu, Christina |
| contents | We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or decay, according to the strength of spatially nonlocal intra- and interspecific interactions. The two cell phenotypes are interchangeable, the transitions depending on the environmental acidity. We prove global existence of a weak solution to the considered PDE-ODE-PDE system and perform numerical simulations in 1D to informally investigate boundedness and patterning behavior in dependence of the system's parameters and kernels involved in the nonlocal terms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_12657 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a PDE-ODE-PDE model for two interacting cell populations under the influence of an acidic environment and with nonlocal intra- and interspecific growth limitation Eckardt, Maria Surulescu, Christina Analysis of PDEs 35K20, 35K57, 35Q92, 92C17 We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or decay, according to the strength of spatially nonlocal intra- and interspecific interactions. The two cell phenotypes are interchangeable, the transitions depending on the environmental acidity. We prove global existence of a weak solution to the considered PDE-ODE-PDE system and perform numerical simulations in 1D to informally investigate boundedness and patterning behavior in dependence of the system's parameters and kernels involved in the nonlocal terms. |
| title | On a PDE-ODE-PDE model for two interacting cell populations under the influence of an acidic environment and with nonlocal intra- and interspecific growth limitation |
| topic | Analysis of PDEs 35K20, 35K57, 35Q92, 92C17 |
| url | https://arxiv.org/abs/2409.12657 |