James C. Robinson

email: j.c.robinson@warwick.ac.uk


MASDOC A1: LINEAR PARTIAL DIFFERENTIAL EQUATIONS

MASDOC: The current version of the A1 notes (9/12/10) are here. Please let me know of any errors/incosistencies. The old Functional Analysis I webpage may be useful.

Examples sheets: One, Two, and Three, Four, Five.

Assessed questions should be with be by the end of Wednesday 12th January. [Sheet 1: 3,6, and 12; Sheet 2: 1, 8, and 13; Sheet 3: 4, 7, and 10; Sheets 4 & 5 as starred on the sheet.]

ASSESSED QUESTIONS: CORRECTIONS & HINTS

Sheet 1: Q12 should read $(Au,v)=(u,A^*v)$

Sheet 2: Q13 do not forget to check that you really have the weak derivative

Sheet 3: Q7 For correct formulation of this question see the solutions

Sheet 4: Q3 Should be $|\alpha|=k$ rather than $|\alpha|=k+1$; Q4 find the weak form by taking the inner product with some $\phi\in C^\infty(\Omega)$; Q5 $\lambda_0=0$

Sheet 5: Do Q3 rather than Q1

SOLUTIONS to the problems (apart from the assessed questions!) are here.

ORALS will be on Monday 10th January (first day of term). Please sign up on the sheet just outside my office (C2.20). Here are some guidelines to tell you what to expect.

The Infinite-dimensional dynamical systems (2007 course) lecture notes are here.

PUBLICATIONS

BOOKS

  • with P.A. Glendinning (eds.): From Finite to Infinite Dimensional Dynamical Systems, proceedings of the NATO ASI workshop at the Isaac Newton Institute, August 1995. Kluwer Academic, 2001.

    Book

  • Infinite-dimensional dynamical systems, Cambridge University Press "Texts in Applied Mathematics" Series (2001).

    Book

  • An Introduction to Ordinary Differential Equations, Cambridge University Press 2004.

    Book

  • with J.L. Rodrigo (eds.): Partial Differential Equations and Fluid Mechanics, LMS Lecture Note Series 264, Cambridge University Press 2009.

    Book

  • Dimensions, Embeddings, and Attractors, Cambridge Tracts in Mathematics 186, Cambridge University Press 2011.

    Book

  • LECTURE NOTES

  • Some approaches to finite-dimensional behaviour in the Navier-Stokes Equations, lectures given at the University of Seville, Easter 1997.
  • Topics in Mathematical Phsyics: a 4th year lecture course at Warwick based on my book, Infinite-Dimensional Dynamical Systems.
  • Attractors and finite-dimensional behaviour in the Navier-Stokes equations, notes for lectures given at the ICMS Instructional Conference on Mathematical Hydrodynamics, June 2003.
  • The Navier-Stokes equations, Lectures given at the AARMS Summer school at Memorial University, Newfoundland, July/August 2003