03600nam 22006375 450 991074369350332120240619151504.03-031-35976-310.1007/978-3-031-35976-7(CKB)28103158600041(MiAaPQ)EBC30723212(Au-PeEL)EBL30723212(DE-He213)978-3-031-35976-7(PPN)272261297(EXLCZ)992810315860004120230829d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA Compact Course on Linear PDEs /by Alberto Valli2nd ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (267 pages)La Matematica per il 3+2,2038-5757 ;1549783031359750 1. Introduction -- 2. Second order linear elliptic equations -- 3. A bit of functional analysis -- 4. Weak derivatives and Sobolev spaces -- 5. Weak formulation of elliptic PDEs -- 6. Technical results -- 7. Additional results -- 8. Saddle points problems -- 9. Parabolic PDEs -- 10. Hyperbolic PDEs -- Appendix A: Partition of unity -- Appendix B: Lipschitz continuous and smooth domains -- Appendix C: Integration by parts for smooth functions and vector fields -- Appendix D: Reynolds transport theorem -- Appendix E: Gronwall lemma -- Appendix F: Necessary and sufficient conditions for the well-posedness of the variational problem.This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations. .La Matematica per il 3+2,2038-5757 ;154Differential equationsMathematicsData processingFunctional analysisDifferential EquationsComputational Mathematics and Numerical AnalysisFunctional AnalysisEquacions en derivades parcialsthubAnàlisi funcionalthubLlibres electrònicsthubDifferential equations.MathematicsData processing.Functional analysis.Differential Equations.Computational Mathematics and Numerical Analysis.Functional Analysis.Equacions en derivades parcialsAnàlisi funcional515.353Valli Alberto8376MiAaPQMiAaPQMiAaPQBOOK9910743693503321Compact Course on Linear PDEs2983604UNINA