Proceedings of the American Mathematical Society · 2000 · 28 citations · 6 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsPopulation BiologyDiffusion ProcessesExistence TheoryNonlinear DynamicsPopulation DynamicsPopulation PersistenceReaction-diffusion SystemsFinite TimeLong-time BehaviorNonlinear DiffusionNonlinear Diffusion EquationsNonlinear EvolutionParabolic Partial Differential EquationsReaction-diffusion EquationsUniqueness In Nonlinear Differential Equations
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.
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