LEADER 03858nam 22007333 450 001 996466416103316 005 20230718153649.0 010 $a3-030-89397-9 035 $a(CKB)5860000000000175 035 $a(MiAaPQ)EBC6882488 035 $a(Au-PeEL)EBL6882488 035 $a(OCoLC)1299382308 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/78269 035 $a(PPN)260825611 035 $a(EXLCZ)995860000000000175 100 $a20220321d2022 fy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEvolutionary equations $ePicard's theorem for partial differential equations, and applications /$fChristian Seifert, Sascha Trostorff, Marcus Waurick 210 $aCham$cSpringer Nature$d2022 210 1$aCham :$cSpringer International Publishing AG,$d2022. 210 4$d©2022. 215 $a1 online resource (321 pages) 225 1 $aOperator theory, advances and applications$vv.287 311 1 $a3-030-89396-0 327 $aIntroduction -- Unbounded Operators -- The Time Derivative -- Ordinary Differential Equations -- The Fourier-Laplace Transformation and Material Law Operators -- Solution Theory for Evolutionary Equations -- Examples of Evolutionary Equations -- Causality and a Theorem of Paley and Wiener -- Initial Value Problems and Extrapolation Spaces -- Differential Algebraic Equations -- Exponential Stability of Evolutionary Equations -- Boundary Value Problems and Boundary Value Spaces -- Continuous Dependence on the Coefficients I -- Continuous Dependence on the Coefficients II 330 $aThis open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research. 410 0$aOperator theory, advances and applications,$v287. 606 $aDifferential equations 606 $aEquacions d'evolució$2thub 606 $aEquacions en derivades parcials$2thub 608 $aLlibres electrònics$2thub 610 $aOpen Access 610 $aEvolutionary equations 610 $aMaxwell's equations 610 $aInitial Boundary Value Problems 610 $aMathematical Physics 610 $aHilbert space approach 610 $aHeat Equation 610 $aWave Equation 610 $aElasticity 610 $aDifferential Algebraic Equations 610 $aExponential Stability 610 $aHomogenisation 610 $aEvolutionary Inclusions 610 $aTime-dependent partial differential equations 610 $aCoupled Systems 610 $aCausality 615 0$aDifferential equations. 615 7$aEquacions d'evolució 615 7$aEquacions en derivades parcials 700 $aSeifert$b Christian$01214744 701 $aTrostorff$b Sascha$f1984-$01258807 701 $aWaurick$b Marcus$0721074 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466416103316 996 $aEvolutionary equations$92916996 997 $aUNISA