Affiliations: Department of Mathematics, International Solomon University, Golosiivska 12, Kiev, Ukraine | School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel | Department of Mathematics, Voronezh Technical University, Moscow Prospekt 14, Voronezh, Russia
Abstract: This paper is devoted to the investigation of classes of uniqueness for classical solutions of the Cauchy problem \begin{eqnarray} && \rho (t,x)\curpartial_{t}u=\sum\limits^{n}_{i,j=1}a_{ij}(t,x)\curpartial_{x_{i}} \curpartial_{x_{j}}u +\sum\limits^{n}_{i=1}b_{i}(t,x)\curpartial_{x_{i}}u+c(t,x)u,\\ && u\vert_{t=0}=u_{0}(x),\quad x\in R^{n} . \end{eqnarray}
We study how the behaviour of the function \rho(t,x) as \vert x\vert \to \infty influences the classes of uniqueness of the Cauchy problem. In particular the dependence of such classes on the number of the space coordinates is clarified. We also discuss the sharpness of the obtained results.
