Diffusion phenomena for partially dissipative hyperbolic systems (Q2792112)

The Cauchy problem for a hyperbolic system of differential equations with time dependent coefficients satisfying some self-adjointness, dissipativity and uniform Kalman conditions is considered first. A parabolic equation is associated to the system. If \(U(t,x)\) denotes the solution to the hyperbolic system, \(w(t,x)\) the solution to the parabolic equation and \(K(t,D)\) a vector of second order differential operators, an \(L^2\)-estimate for the difference \(U(t,\cdot)-K(t,D)w(t,\cdot)\) is proved. These type of estimates should show that under some special conditions, solutions to a dissipative hyperbolic system are asymptotically equivalent to solutions of a corresponding parabolic equation.NEWLINENEWLINEFor the entire collection see [Zbl 1321.35002].