Degenerate parabolic equations whose coefficients are increasing (Q909885)

The following equation generalizing that of diffusion with inertia and dissipation is considered \[ \partial u(t,R)/\partial t+\sum^{n}_{j=1}(x_ j\partial u(t,R)/\partial y_ j+y_ j\partial u(t,R)/\partial z_ j)=\sum_{| k| \leq 2b}A_ k(t,R)D^ k_ xu(t,R)+ \] \[ +\sum_{| k| \leq 2b-1}\tilde A_ k(t,R)D^ k_ xu(t,R)=P(t,R;D_ x)u(t,R)+\tilde P(t,R;D_ x)u(t,R),\quad R=(x,y,z)\in {\mathbb{R}}^{3n} \] under suitable conditions for the coefficients. The existence of the fundamental solution is proved and certain estimates of this solution are given.