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Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations |
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| Authors: | Azmy S Ackleh Lan Ke |
| Institution: | Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010 ; Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010 |
| Abstract: | We establish existence and uniqueness of solutions for a general class of nonlocal nonlinear evolution equations. An application of this theory to a class of nonlinear reaction-diffusion problems that arise in population dynamics is presented. Furthermore, conditions on the initial population density for this class of problems that result in finite time extinction or persistence of the population is discussed. Numerical evidence corroborating our theoretical results is given. |
| Keywords: | Nonlocal parabolic evolution equations unbounded diffusion population dynamics asymptotic behavior extinction persistence |
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