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A diffusive logistic equation with concentrated and nonlocal sources
Author(s) -
Caicedo A.,
Cruz F. W.,
Limeira R.,
Viana A.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4447
Subject(s) - mathematics , logistic function , nonlinear system , diffusion , diffusion equation , mathematical analysis , lebesgue integration , reaction–diffusion system , statistics , economy , thermodynamics , economics , physics , service (business) , quantum mechanics
In this paper, we study a reaction‐diffusion equation where nonlinear memory and concentration effects are considered at the same time. We are specially concerned with the local solvability of this problem for singular initial data in Lebesgue spaces. We also analyze the vanishing concentration problem and prove a blow‐up alternative. Copyright © 2017 John Wiley & Sons, Ltd.