000 03163nam a22004815i 4500
001 978-3-319-02000-6
003 DE-He213
005 20140220082840.0
007 cr nn 008mamaa
008 131122s2013 gw | s |||| 0|eng d
020 _a9783319020006
_9978-3-319-02000-6
024 7 _a10.1007/978-3-319-02000-6
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aDenk, Robert.
_eauthor.
245 1 0 _aGeneral Parabolic Mixed Order Systems in Lp and Applications
_h[electronic resource] /
_cby Robert Denk, Mario Kaip.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2013.
300 _aVIII, 250 p. 16 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOperator Theory: Advances and Applications,
_x0255-0156 ;
_v239
505 0 _aIntroduction 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.
520 _aIn 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.
650 0 _aMathematics.
650 0 _aOperator theory.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aMathematical Physics.
650 2 4 _aOperator Theory.
700 1 _aKaip, Mario.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319019994
830 0 _aOperator Theory: Advances and Applications,
_x0255-0156 ;
_v239
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-02000-6
912 _aZDB-2-SMA
999 _c96570
_d96570