Geodesic
Existence of solution of a free boundary problem for reaction-diffusion systems
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 716-731.

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In this paper, we prove the existence of solution of a novel free boundary problem for reaction-diffusion systems describing growth of biological tissues due to cell influx and proliferation. For this aim, we transform it into a problem with fixed boundary, through a change of variables. The new problem thus obtained has space and time dependent coefficients with nonlinear terms. We then prove the existence of solution for the corresponding linear problem, and deduce the existence of solution for the nonlinear problem using the fixed point theorem. Finally, we return to the problem with free boundary to conclude the existence of its solution.
Keywords: free boundary problem, growth of biological tissues
Mots-clés : reaction-diffusion system, existence of solution. 
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G. A. Younes; N. El Khatib; V. A. Volpert. Existence of solution of a free boundary problem for reaction-diffusion systems. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 716-731. http://geodesic.mathdoc.fr/item/CMFD_2022_68_4_a10/

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