THE VANISHING VISCOSITY LIMIT ON A MODEL OF KAREIVA-ODELL TYPE IN 2D

. In this paper we invoke the idea of vanishing viscosity limit to bridge the strong solutions of two models in 2D case, i.e., a model of KareivaOdell type in which predators have a remarkable tendency of moving towards diffusible prey, and a model of Stevens-Othmer type where a species has an oriented movement toward a nondiffusing signal. In more detail, we first give in L & INFIN;(& omega;) a uniform-in-& epsilon; upper bound of the unique (for each fixed diffusion coefficient & epsilon; of prey) classical solution of a model of Kareiva-Odell type for any & epsilon; & ISIN; (0, 1). Then we make Lp estimates on the classical solutions to derive a quantitative description in the sense of strong solution. Via the estimates made for the Kareiva-Odell type model, we use Aubin-Lions lemma to show a convergence as & epsilon; & RARR; 0. Finally, we find that the limit of this convergence is a strong solution and also a unique classical solution of a corresponding Stevens-Othmer type model.