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Chamorro, Diego; Meunier, Nicolas

Analysis of a nonlocal and nonlinear system for cell-cell communication. (English) Zbl 07925612

Acta Appl. Math. 193, Paper No. 7, 24 p. (2024).
Summary: We consider a system of two nonlocal and nonlinear partial differential equations that describe some aspects of yeast cell-cell communication. We study local and global existence and uniqueness of solutions. We consider mild solutions and we perform bilinear and trilinear fixed point arguments in suitable functional spaces.

MSC:

35A01 Existence problems for PDEs: global existence, local existence, non-existence
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C37 Cell biology
47J26 Fixed-point iterations

Keywords:

existence problems for PDEs: global existence; local existence; cell communication and cell polarization
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References:

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