A nonlinear system to model communication between yeast cells during their mating process. (English) Zbl 1542.35076
Summary: In this work, we develop a model to describe some aspects of communication between yeast cells. It consists in a coupled system of two one-dimensional non-linear advection-diffusion equations in which the advective field is given by the Hilbert transform. We give some sufficient condition for the blow-up in finite time of the coupled system (formation of a singularity). We provide a biological interpretation of these mathematical results.
{© 2024 IOP Publishing Ltd & London Mathematical Society}
{© 2024 IOP Publishing Ltd & London Mathematical Society}
MSC:
| 35B44 | Blow-up in context of PDEs |
| 35K45 | Initial value problems for second-order parabolic systems |
| 35K58 | Semilinear parabolic equations |
| 35R09 | Integro-partial differential equations |
| 92C37 | Cell biology |
| 47J26 | Fixed-point iterations |
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