Abstract Using the operator splitting method Christov Pontes developed a second order in time implicit di erence scheme for solving the Swift Hohenberg equation S H which describes pattern formation in Rayleigh Benard cells For each time step the scheme involves internal iterations which improve the stability and increase the accuracy with which the Lyapunov functional for S H is approximated D...

The Cauchy problem for a quasilinear system of hyperbolic-parabolic equations is addressed with the method linearization and fixed point. Coupling between hyperbolic parabolic variables allowed in we do not assume Friedrich's symmetrizability system. This coupling results linear energy estimates that prevent application Banach's contraction principle. A metric point theorem developed order to c...