Communications of the
Korean Mathematical Society CKMS

Using calculus inequalities and embedding theorems in $R^1$, we establish $W^1_2$-estimates for the solutions of prey-predator population model with cross-diffusion and self-diffusion terms. Two cases are considered ; (i) $d_1=d_2$, $\al_{12}=\al_{21}=0$, and (ii) $0<\al_{21}<\al_{12}

Keywords: prey-predator system, cross-diffusion, self-diffusion, calculus inequalities, uniform bound, Liapunov functional, convergence

MSC numbers: 35K55, 35B40