Coefficient estimates for global solutions of the Cauchy problem for semilinear systems of partial differential equations (Q2703974)

This paper concerns the Cauchy problem for semilinear first-order systems of the type NEWLINE\[NEWLINE{\partial u\over\partial t}- \sum^n_{k=1} c_k(t,x){\partial u\over\partial x_k}= f(t, x,u),\quad x\in\mathbb{R}^n,\;u\in\mathbb{R}^m.NEWLINE\]NEWLINE By means of a scalar majorant problem there are proved a priori estimates which restrict the growth of the solutions and, hence, guarantee the global existence of the solutions.