Nonexistence of coexisting steady‐state solutions of Dirichlet problem for a cross‐diffusion model. (22nd October 2018)

• Record Type: Journal Article
• Authors: Zhu, Ningning; Tang, De
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 1(2019)
• Page Start: 346
• Page End: 353
• Publication Date: 2018-10-22
• Subjects: cross‐diffusion -- Dirichlet boundary condition -- SKT model -- steady‐state solution; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5350
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We study a special case of Shigesada–Kawasaki–Teramoto (SKT) model for two competing species with the Dirichlet boundary conditions. In our case, one of the species is not influenced by self‐diffusion or cross‐diffusion. We specify the explicit range of parameters by contradiction such that there are no coexisting steady‐state solutions to the model.