On some differential inequalities and the uniqueness of global semiclassical solutions to the Cauchy problem for weakly-coupled systems (Q1277350)

The authors consider some partial differential inequalities of Haar type \[ |u_t|\leq M|\nabla_x u|+\rho(t,|u|), \] with \( \rho\in C^0\). They combine the method of multifunction and differential inclusions (see \textit{T. D. Van} and \textit{N. D. Thai Son} [Proc. Am. Math. Soc. 121, No. 3, 865-870 (1994; Zbl 0818.35018)]; \textit{T. D. Van} and \textit{N.~D.~Thai Son} [Differential Equations 30, No.~4, 659-666 (1994); translation from Differ. Uravn. 30, No.~4, 712-719 (1994; Zbl 0826.35019)]) with the technique of Carathéodory comparison equations and prove some new uniqueness criteria for weakly coupled systems.