Lecture Series

This page groups sessions by Lecture Series adding global information about the series when available.

This is an introductory course on the wave equation, to be delivered in weekly two-hour sessions.

Topics to be covered include Fourier and physical space methods, existence and uniqueness of solutions to linear equations with constant or variable coefficients, energy estimates, vector fields, Strichartz estimates and local/global well posedness for nonlinear wave equations. Time permitting, singularity formation and geometric optics may also be addressed.

References

General PDE books with relevant sections

• G. Folland, "Introduction to Partial Differential Equations", 2nd Ed., Princeton Univ. Press, 1995
• F. John, "Partial Differential Equations", 4th ed., Springer, 1981.
• J. Rauch, "Partial Differential Equations", Springer, 1991.
• M. Taylor, "Partial Differential Equations, I — Basic Theory", 2nd ed., Springer 2012.
• F. Trèves, "Basic Linear Partial Differential Equations", Academic Press 1975, reprint Dover 2013.

Books on wave equations

• C. Sogge, "Lectures on Nonlinear Wave Equations", 2nd Ed., International Press, 2013.
• S. Alinhac, "Hyperbolic Partial Differential Equations", Springer, 2009.
• L. Hormander, "Lectures on Nonlinear Hyperbolic Equations", Springer 1997.
• P. Lax, "Hyperbolic Partial Differential Equations", Courant Lecture Notes, AMS, 2006.
• T. Tao, "Nonlinear Dispersive Equations, Local and Global Analysis", AMS, 2006.

Online lecture notes

• S. Selberg, https://www.researchgate.net/publication/267944898_Lecture_Notes_Math_632_PDE
• A. Shao, https://lpde.maths.qmul.ac.uk/a.shao/research/notes.php
• J. Luk, https://web.stanford.edu/~jluk/NWnotes.pdf
• H. Ringstrom, https://people.kth.se/~hansr/nlw.pdf

Specific or advanced references

• S. Alinhac, "Geometric Analysis of Hyperbolic Differential Equations, An Introduction", Cambridge University Press, 2010.
• S. Alinhac, "Blowup for Nonlinear Hyperbolic Equations", Birkauser, 1995.
• J. Shatah, M. Struwe, "Geometric Wave Equations", Courant Lecture Notes, AMS, 2000.
• J. Rauch, "Hyperbolic Partial Differential Equations and Geometric Optics", AMS, 2012.
• F. Friedlander, "The Wave Equation on a Curved Space-Time", Cambridge University Press, 2010.