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On a nonlinear renewal equation with diffusion
Author(s) -
Kakumani Bhargav Kumar,
Tumuluri Suman Kumar
Publication year - 2016
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.3511
Subject(s) - mathematics , uniqueness , nonlinear system , eigenfunction , term (time) , type (biology) , population , exponential function , mathematical analysis , eigenvalues and eigenvectors , ecology , physics , demography , quantum mechanics , sociology , biology
In this paper, we consider a nonlinear age structured McKendrick–von Foerster population model with diffusion term. Here we prove existence and uniqueness of the solution of the equation. We consider a particular type of nonlinearity in the renewal term and prove Generalized Relative Entropy type inequality. Longtime behavior of the solution has been addressed for both linear and nonlinear versions of the equation. In linear case, we prove that the solution converges to the first eigenfunction with an exponential rate. In nonlinear case, we have considered a particular type of nonlinearity that is present in the mortality term in which we can predict the longtime behavior. Copyright © 2015 John Wiley & Sons, Ltd.