arXiv subjects

Rana D. Parshad

Publications and source records attributed to Rana D. Parshad.

38 records · Page 3Linked to original sources

arXiv2014

Global existence for a strongly coupled reaction diffusion system

In this work we use functional methods to prove the boundedness and global existence of solutions for a class of strongly coupled parabolic systems. We apply the results to deduce the global existence of solutions for a classic Shigesada-Kawasaki-Teramoto (SKT) type model, for an extended range of the self-diffusion and cross-diffusion coefficients than those available in the current literature. We provide numerical simulations in 2D, via a spectral Galerkin method to verify our global existence results, as well as to visualize the dynamics of the system.

math.AP↗

arXiv2014

A remark on "Study of a Leslie-Gower-type tritrophic population model" [Chaos, Solitons and Fractals 14 (2002) 1275-1293]

In [Aziz-Alaoui, 2002] a three species ODE model, based on a modified Leslie-Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in [Aziz-Alaoui, 2002], if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations.

math.DS↗