Abstract
This paper deals with positive solutions of degenerate and strongly coupled quasilinear parabolic systems u t = v α Δ u + u ( a 1 − b 1 u + c 1 v ) , v t = u β Δ v + v ( a 2 + b 2 u − c 2 v ) with null Dirichlet boundary condition and positive initial conditions describing a cooperating two-species Lotka–Volterra model with cross-diffusion, where the constants a i , b i , c i > 0 for i = 1 , 2 and α, β are non-negative. The local existence of positive classical solutions is proved. Moreover, the authors proved that the solutions are global if intra-specific competition of the species are strong, whereas the solutions may blow up if the inter-specific cooperation are strong and α , β ⩽ 1 .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.