General Parabolic Mixed Order Systems in Lp and Applications [Hardcover]

In this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixed-order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in Lp-Lq-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity) which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations which are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer Lp-Sobolev spaces as Besov spaces, Bessel potential spaces, and TriebelLizorkin spaces. The last-mentioned class appears in a natural way as traces of Lp-Lq-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic plate equation, the two-phase NavierStokes equations with BoussinesqScriven surface, and the Lp-Lq two-phase Stefan problem with GibbsThomson correction.This text establishes a theory for general linear parabolic partial differential equations that covers equations with inhomogeneous symbol structure as well as mixed-order systems.Introduction and Outline.- 1?The joint time-space H(infinity)-calculus.- 2 The Newton polygon approach for mixed-order systems.-3 Triebel-Lizorkin spaces and the Lp-Lq setting.-?4 Application to parabolic differential equations.- List of figures.-Bibliography.- List of symbols.- Index. In this text, a theory for general linear parabolic partial differential equations is established, which covers equations with inhomogeneous symbol structure as well as mixed order systems. Typical applications include several variants of the Stokes system and free boundl#,