Some stabilization theorems for solutions of the Cauchy problem for Shilov-parabolic systems in classes of generalized functions (Q1114859)

The author considers the system \[ \partial u_ i(t,x)/\partial t=\sum^{N}_{j=1}\sum_{| k| \leq \rho}a_ k^{ij}(t)D^ k_ x u_ j(t,x),\quad i=1,...,N, \] with continuous bounded coefficients and parabolic in Shilov's sense in the space \([0,T]\times R^ n\). Sufficient (and in some cases also necessary) stability conditions of the Cauchy problem in the class of generalized functions are established.