An ultraparabolic problem arising from age-dependent population diffusion (Q1034174)

The initial-boundary problem for ultraparabolic equation \(u_t (t, a, x) + u_a (t, a, x) = - d(t, a, x)+\Delta u(t, a, x)\), \(t>0\), \(a>0\), \(x\in\Omega\) is under consideration. In this paper authors prove existence, uniqueness and continuous dependence upon the data as well as regularity of solutions with respect to space variables.