Abstract
We investigate the global time existence of smooth solutions for the Shigesada- Kawasaki-Teramoto system of cross-diffusion equations of two competing species in population dynamics. If there are self-diffusion in one species and no cross-diffusion in the other, we show that the system has a unique smooth solution for all time in bounded domains of any dimension. We obtain this result by deriving global W1,p-estimates of Calderón-Zygmund type for a class of nonlinear reaction-diffusion equations with self-diffusion. These estimates are achieved by employing the Caffarelli-Peral perturbation technique together with a new two-parameter scaling argument.
Original language | English |
---|---|
Pages (from-to) | 2122-2177 |
Number of pages | 56 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 47 |
Issue number | 3 |
DOIs | |
State | Published - 2015 |
Keywords
- Calderón- Zygmund type estimates
- Cross-diffusion system
- Global existence
- Global regularity
- Gradient estimates
- SKT system