An intrinsic metric approach to uniqueness of the positive Cauchy problem for parabolic equations (Q1384607)

We investigate uniqueness of nonnegative solutions of the Cauchy problem for second order parabolic equations \[ {\partial\over \partial t} u=\sum^N_{i,j=1} {\partial\over \partial x_j} \left(a_{ij} (x,t) {\partial\over \partial x_i}u\right) +\sum^N_{i=1} b_i(x,t) {\partial\over \partial x_i} u-V(x,t)u \] in \(\mathbb{R}^N \times(0,T)\), \(0<T<\infty\). In terms of the intrinsic metric of a parabolic equation, we give maximal growth rates of the coefficients of the parabolic equation whose nonnegative solution with initial data zero is identically zero.