Multi-phase Stefan problems for a nonlinear 1-d model of cell-to-cell adhesion and diffusion - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: We consider a family of multi-phase Stefan problems for a certain 1-d modelof cell-to-cell adhesion and diffusion, which takes the form of a nonlinearforward-backward parabolic equation. In each material phase the cell densitystays either high or low, and phases are connected by jumps across an`unstable- interval. We develop an existence theory for such problems whichallows for the annihilation of phases and the subsequent continuation ofsolutions. Stability results for the long-time behaviour of solutions are alsoobtained, and, where necessary, the analysis is complemented by numericalsimulations.



Author: K. Anguige

Source: https://arxiv.org/







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