LEADER 03871nam 2200709 a 450 001 9910786015603321 005 20230803025303.0 010 $a3-11-026905-8 024 7 $a10.1515/9783110269055 035 $a(CKB)2670000000328353 035 $a(EBL)955848 035 $a(OCoLC)828137762 035 $a(SSID)ssj0000827078 035 $a(PQKBManifestationID)11450293 035 $a(PQKBTitleCode)TC0000827078 035 $a(PQKBWorkID)10829533 035 $a(PQKB)10717951 035 $a(MiAaPQ)EBC955848 035 $a(DE-B1597)173762 035 $a(OCoLC)1013956845 035 $a(OCoLC)853261071 035 $a(DE-B1597)9783110269055 035 $a(Au-PeEL)EBL955848 035 $a(CaPaEBR)ebr10649221 035 $a(CaONFJC)MIL503228 035 $a(EXLCZ)992670000000328353 100 $a20121026d2013 uy 0 101 0 $aeng 135 $aur|nu---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aLinear and semilinear partial differential equations$b[electronic resource] $ean introduction /$fRadu Precup 210 $aBerlin $cRadu Precup De Gruyter$d[2013] 215 $a1 online resource (296 p.) 225 0 $aDe Gruyter Textbook 225 0$aDe Gruyter textbook 300 $aDescription based upon print version of record. 311 $a3-11-026904-X 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tNotation --$tContents --$tPart I. Classical Theory --$tChapter 1. Preliminaries --$tChapter 2. Partial Differential Equations and Mathematical Modeling --$tChapter 3. Elliptic Boundary Value Problems --$tChapter 4. Mixed Problems for Evolution Equations --$tChapter 5. The Cauchy Problem for Evolution Equations --$tPart II. Modern Theory --$tChapter 6. Distributions --$tChapter 7. Sobolev Spaces --$tChapter 8. The Variational Theory of Elliptic Boundary Value Problems --$tPart III. Semilinear Equations --$tChapter 9. Semilinear Elliptic Problems --$tChapter 10. The Semilinear Heat Equation --$tChapter 11. The Semilinear Wave Equation --$tChapter 12 Semilinear Schrödinger Equations --$tBibliography --$tIndex 330 $aThe text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems. 410 3$aDe Gruyter Textbook 606 $aDifferential equations, Linear$vTextbooks 606 $aDifferential equations, Partial$vTextbooks 610 $aElliptic Equation. 610 $aHeat Equation. 610 $aPartial Differential Equation. 610 $aSobolev Space. 610 $aWave Equation. 615 0$aDifferential equations, Linear 615 0$aDifferential equations, Partial 676 $a515/.353 686 $aSK 500$2rvk 700 $aPrecup$b Radu$0737781 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786015603321 996 $aLinear and semilinear partial differential equations$93702129 997 $aUNINA