A result of uniqueness of solutions of the Shigesada-Kawasaki-Teramoto equations (Q2417223)

Shigesada-Kawasaki-Teramoto (SKT) systems arise in models of population dynamics. SKT systems are cross-diffusion systems exhibiting strong nonlinear coupling and lack the maximum principle. The authors demonstrate uniqueness of weak solutions to SKT using a method that relies on the associated adjoint problem to create test functions to establish uniqueness [\textit{D. Aronson} et al., Nonlinear Anal., Theory Methods Appl. 6, 1001--1022 (1982; Zbl 0518.35050)]. These weak solutions belong to \(L^\infty(0,T;H^1(\Omega)^2)\) with time-derivatives in \(L^{4/3}(\Omega_T)^2\) and \(d\le4\).