On solution uniqueness for initial-boundary value problem for a system of second order nonlinear parabolic equations in an unbounded domain (Q1311188)

A comparison theorem for an initial-boundary value problem to a system of nonlinear parabolic equations \[ u^i_t (x,t) = f^i(x,t,u_1, \ldots, u_m,\;u^i_x, u^i_{xx}), \;i = 1, \ldots, m,\;x \in \Omega \subset \mathbb{R}^n, \;t \in (0,T] \] is proved in a class of functions which tend to zero at infinity, \(\Omega\) is an unbounded domain and \(f_i\) satisfy elliptic and quasimonotonicity conditions.