Existence of pulses for a reaction-diffusion system of blood coagulation

Nicolas Ratto, Martine Marion, Vitaly A. Volpert

DOI: http://dx.doi.org/10.12775/TMNA.2019.067

Abstract


The paper is devoted to the investigation of a reaction-diffusion system of equations describing the process of blood coagulation. Existence of pulse solutions, that is, positive stationary solutions with zero limit at infinity is studied. It is shown that such solutions exist if and only if the speed of the travelling wave described by the same system is positive. The proof is based on the Leray-Schauder method using topological degree for elliptic problems in unbounded domains and a priori estimates of solutions in some appropriate weighted spaces.

Keywords


Reaction-diffusion system; blood coagulation; existence of pulses; Leray-Schauder method

Full Text:

PREVIEW FULL TEXT

References


T. Galochkina, H. Ouzzane, A. Bouchnita and V. Volpert, Traveling wave solutions in the mathematical model of blood coagulation, Appl. Anal. 96 (2017), no. 16, 2891–2905.

Y.V. Krasotkina, E.I. Sinauridze and F.I. Ataullakhanov, Spatiotemporal dynamics of fibrin formation and spreading of active thrombin entering non-recalcified plasma by diffusion, Biochimica et Biophysica Acta (BBA) – General Subjects 1474 (2000), no. 3, 337–345.

M. Marion and V. Volpert, Existence of pulses for a monotone reaction-diffusion system, Pure Appl. Funct. Anal. (2016).

E.A. Pogorelova and A.I. Lobanov, Influence of enzymatic reactions on blood coagulation autowave, Biophysics 59 (2014), no. 1, 110–118.

A.A. Tokarev, Y.V. Krasotkina, M.V. Ovanesov, M.A. Panteleev, M.A. Azhigirova, V.A. Volpert, F.I. Ataullakhanov and A.A. Butilin, Spatial dynamics of contact-activated fibrin clot formation in vitro and in silico in haemophilia b: Effects of severity and ahemphil b treatment, Math. Modelling Natural Phenomena 1 (2006), no. 2, 124–137.

V.A. Volpert, Elliptic partial differential equations, Volume 1. Fredholm theory of elliptic problems in unbounded domains, Birkhäuser, Basel, 2011.

V.A. Volpert and A.I. Volpert, Spectrum of elliptique operators and stability of travelling waves. Asymptotic Analysis, 2000.

A.I. Volpert, V.A. Volpert and V.A. Volpert, Traveling Wave Solution of Parabolic Systems, Vol. 140, 1994.

V.I. Zarnitsina, F.I. Ataullakhanov, A.I. Lobanov and O.L. Morozova, Dynamics of spatially nonuniform patterning in the model of blood coagulation. Chaos: An Interdisciplinary, J. Nonlinear Sci. 11 (2001), no. 1, pp. 57.


Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism