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Initiation of reaction-diffusion waves of blood coagulation. (English) Zbl 1398.35117

Summary: Formation of blood clot in response to the vessel damage is triggered by the complex network of biochemical reactions of the coagulation cascade. The process of clot growth can be modeled as a traveling wave solution of the bistable reaction-diffusion system. The critical value of the initial condition which leads to convergence of the solution to the traveling wave corresponds to the pulse solution of the corresponding stationary problem. In the current study, we prove the existence of the pulse solution for the stationary problem in the model of the main reactions of the blood coagulation cascade using the Leray-Schauder method.

MSC:

35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
92C05 Biophysics
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