PDE-CDT Core Course Analysis of Partial Differential...
Transcript of PDE-CDT Core Course Analysis of Partial Differential...
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EPSRC Centre for Doctoral Training inPartial Differential Equations
Trinity Term28 April – 14 June 2017 (16 hours)
Final Exam: 19-20 June 2017 Course format: Teaching Course (TT)
By Prof. Gui-Qiang G. ChenProf. Wei Xiang
PDE-CDT Core Course
Analysis of Partial Differential Equations-Part III
Lecture 4
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Bressan, A.: Hyperbolic Systems of Conservation Laws.The One-Dimensional Cauchy Problem. Oxford University Press: Oxford, 2000.
Dafermos, C: Hyperbolic Conservation Laws in ContinuumPhysics, 3rd Edition, Springer-Verlag: Berlin, 2010.
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Functional Analytic Approaches for the Existence Theory:
• Compensated Compactness • Weak Convergence Methods• Geometric Measure Arguments• ……
1. C. M. Dafermos: Hyperbolic Conservation Laws in Continuum Physics,
Third edition. Springer-Verlag: Berlin, 2010.
2. B. Dacorogna: Weak Continuity and Weak Lower Semicontinuity of Nonlinear
Functionals, Lecture Notes in Mathematics, Vol. 922, 1-120, Springer-Verlag, 1982.
3. L. C. Evans:. Weak Convergence Methods for Nonlinear Partial Differential
Equations. CBMS-RCSM, 74. AMS: Providence, RI, 1990
4. D. Serre, La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations à une dimension d'espace. J. Math. Pures Appl. (9) 65 (1986), 423–468.
5. The references cited therein, especially more recent references.