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E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA377.SPR FCT 81883 (Browse shelf) | 1 | Available |
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QA377.SPR FCT 81797 Dispersive equations and nonlinear waves | QA377.SPR FCT 81798 Elliptic partial differential equations | QA377.SPR FCT 81872 Spectral and high order methods for partial differential equations | QA377.SPR FCT 81883 General parabolic mixed order systems in Lp and applications | QA377.SPR FCT 81888 An invitation to hypoelliptic operators and Hörmander's vector fields | QA377.SPR FCT 81897 Hyperbolic systems with analytic coefficients | QA377.SPR FCT 81948 Analysis and topology in nonlinear differential equations |
Colocação: Online
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 that 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 Triebel–Lizorkin spaces. The latter 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 Navier–Stokes equations with Boussinesq–Scriven surface, and the Lp-Lq two-phase Stefan problem with Gibbs–Thomson correction.
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