The equation mentioned in the title is: \[ Lu=\nu^ 2(t)u_{tt}- \sum^{n}_{i,j=1}\partial /\partial x_ i(a_{ij}(x,t)u_{x_ j})+au_ t+\sum^{n}_{i=1}b_ iu_{x_ i}+cu=f, \] with \(a_{ij}=a_{ji}\), \(\sum^{n}_{i,j=1}a_{ij}\xi_ i\xi_ j\geq 0\), for any \(\xi \in {\mathbb{R}}^ n\). \(\nu\) (t) is continuous on [0,1] and differentiable on (0,1]. It is positive for all \(t>0.\) The author proves the existence and uniqueness of solutions if f(t), \(\nu\) (t) satisfy certain conditions. He discusses the special case \(\nu =t^{m/2}\), \(1\leq m<2\), in some length, offering some estimates as well as a uniqueness theorem valid for some bounds on a norm of f.