LEADER 03735nam 22005055 450 001 996418252003316 005 20200824165852.0 010 $a3-030-47333-3 024 7 $a10.1007/978-3-030-47333-4 035 $a(CKB)4100000011398302 035 $a(MiAaPQ)EBC6318151 035 $a(DE-He213)978-3-030-47333-4 035 $a(PPN)250214792 035 $a(EXLCZ)994100000011398302 100 $a20200824d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Primer for a Secret Shortcut to PDEs of Mathematical Physics$b[electronic resource] /$fby Des McGhee, Rainer Picard, Sascha Trostorff, Marcus Waurick 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (191 pages) 225 1 $aFrontiers in Mathematics,$x1660-8046 311 $a3-030-47332-5 327 $aIntroduction -- The Solution Theory for a Basic Class of Evolutionary Equations -- Some Applications to Models from Physics and Engineering -- But what about the Main Stream? -- Two Supplements for the Toolbox -- Requisites from Functional Analysis. 330 $aThis book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering. As a unique feature, this powerful tool for tackling time-dependent partial differential equations is subsequently applied to many equations. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach. The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in the appendix. The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master?s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality. 410 0$aFrontiers in Mathematics,$x1660-8046 606 $aPartial differential equations 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aPartial differential equations. 615 14$aPartial Differential Equations. 676 $a515.353 700 $aMcGhee$b Des$4aut$4http://id.loc.gov/vocabulary/relators/aut$059781 702 $aPicard$b Rainer$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTrostorff$b Sascha$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWaurick$b Marcus$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418252003316 996 $aA Primer for a Secret Shortcut to PDEs of Mathematical Physics$91965973 997 $aUNISA