Abstract
We consider a class of reaction-diffusion systems with resource-consumer interaction. Such systems have been thoroughly studied in a number of mathematical articles such as those of Alikakos [1], Masuda [10], Haraux and Youkana [6], Hoshino [7] and Kanel [9]. Their main results concern the well-posedness of the parabolic problems, L∞ bounds on the solutions which do not depend on time and a study of their large time behavior; it turns out that the solution pairs converge to constants as t tends to infinity. However their transient behavior may be very complex and phenomena such as tip splitting may occur at intermediate times.
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Feireisl, E., Mimura, M., Hilhorst, D., Weidenfeld, R. (2002). On Some Reaction-Diffusion Systems with Nonlinear Diffusion Arising in Biology. In: Berestycki, H., Pomeau, Y. (eds) Nonlinear PDE’s in Condensed Matter and Reactive Flows. NATO Science Series, vol 569. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0307-0_5
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DOI: https://doi.org/10.1007/978-94-010-0307-0_5
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