Baza Publikacji Pracowników Politechniki Lubelskiej

Status:
Autorzy:	Bobrowski Adam, Lipniacki Tomasz
Dyscypliny:
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Rok wydania:	2019
Wersja dokumentu:	Drukowana \| Elektroniczna
Język:	angielski
Numer czasopisma:	1
Wolumen/Tom:	268
Strony:	239 - 271
Impact Factor:	2,192
Web of Science® Times Cited:	5
Scopus® Cytowania:	7
Bazy:	Web of Science \| Scopus
Efekt badań statutowych	NIE
Materiał konferencyjny:	NIE
Publikacja OA:	NIE
Abstrakty:	angielski
	We consider a singular limit of diffusion equations in 3D domains of thickness converging to zero. In the 2D limit the resulting reaction-diffusion equation has a source term resulting from the Robin-type boundary conditions imposed on boundaries of the original 3D domain. The proposed approach can be applied to constructing approximate solutions of diffusion problems in thin planar, cylindrical, or spherical layers between two membranes. As an example we refer to the problem of activation of B lymphocytes, which typically have large nuclei and a thin cytoplasmic layer which can be considered as a spherical shell. For this example, assuming additionally axial symmetry we provide a rigorous convergence theorem in the language of semigroups of operators.

Robin-type boundary conditions in transition from reaction-diffusion equations in 3D domains to equations in 2D domains