LEADER 05572nam 22007815 450 001 9910299976803321 005 20250609112032.0 010 $a3-0348-0840-2 024 7 $a10.1007/978-3-0348-0840-8 035 $a(CKB)3710000000212206 035 $a(Springer)9783034808408 035 $a(MH)014131695-0 035 $a(SSID)ssj0001298895 035 $a(PQKBManifestationID)11858357 035 $a(PQKBTitleCode)TC0001298895 035 $a(PQKBWorkID)11260502 035 $a(PQKB)10997320 035 $a(DE-He213)978-3-0348-0840-8 035 $a(MiAaPQ)EBC6312231 035 $a(MiAaPQ)EBC5592543 035 $a(Au-PeEL)EBL5592543 035 $a(OCoLC)1066191032 035 $a(PPN)179926365 035 $a(MiAaPQ)EBC1782090 035 $a(EXLCZ)993710000000212206 100 $a20140722d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aVariable Lebesgue Spaces and Hyperbolic Systems /$fby David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (IX, 170 p. 5 illus.)$conline resource 225 1 $aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-0348-0839-9 327 $aPart I: Introduction to the Variable Lebesgue Spaces -- Introduction and motivation -- Properties of variable Lebesgue spaces -- The Hardy-Littlewood maximal operator -- Extrapolation in variable Lebesgue spaces -- Part II: Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems -- Equations with constant coefficients -- Some interesting model cases -- Time-dependent hyperbolic systems -- Effective lower order perturbations -- Examples and counter-examples -- Related topics.    . 330 $aThis book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition. 410 0$aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 606 $aDifferential equations, Partial 606 $aIntegral equations 606 $aFunctions, Special 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 615 0$aDifferential equations, Partial. 615 0$aIntegral equations. 615 0$aFunctions, Special. 615 14$aPartial Differential Equations. 615 24$aIntegral Equations. 615 24$aSpecial Functions. 676 $a515.43 676 $a515.43 700 $aCruz-Uribe$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$066274 702 $aFiorenza$b Alberto$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRuzhansky$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWirth$b Jens$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTikhonov$b Sergey$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299976803321 996 $aVariable Lebesgue Spaces and Hyperbolic Systems$92522979 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress