Announcements


There are no announcements

Forum

General


This course is part of the MAGIC core.

Description

Introduction to the theory of pdes for applied mathematics.
Semester

Spring 2012 (Monday, January 16 to Friday, March 23)

Timetable
  • Mon 11:05 - 11:55
  • Thu 11:05 - 11:55

Lecturer


David Harris
Email david.harris@manchester.ac.uk
Phone (0161) 306 3683
vcard


Students


Photo of  Amnah  Alharbi
Amnah Alharbi
(East Anglia)
Photo of Cisem Bektur
Cisem Bektur
(Loughborough)
Photo of Gokcen Cekic
Gokcen Cekic
(Birmingham)
Photo of Mingliang Cheng
Mingliang Cheng
(Manchester)
Photo of Giovanni Collini
Giovanni Collini
(Cardiff)
Photo of Tom Croft
Tom Croft
(Cardiff)
Photo of Boris Dadachev
Boris Dadachev
(Cardiff)
Photo of Neslihan Delice
Neslihan Delice
(Leeds)
Photo of Aiman Elragig
Aiman Elragig
(Exeter)
Photo of Jhonny Gonzalez
Jhonny Gonzalez
(Manchester)
Photo of Esen hanac
Esen hanac
(Birmingham)
Photo of Stewart Haslinger
Stewart Haslinger
(Liverpool)
Photo of Mazlinda  Ibrahim
Mazlinda Ibrahim
(Liverpool)
Photo of Christopher Jeavons
Christopher Jeavons
(Birmingham)
Photo of Benjamin Lang
Benjamin Lang
(York)
Photo of Fei Liu
Fei Liu
(Liverpool)
Photo of Umberto  Lupo
Umberto Lupo
(York)
Photo of Lavdie Rada
Lavdie Rada
(Liverpool)
Photo of Greg Roddick
Greg Roddick
(Loughborough)
Photo of Ilia Roustemoglou
Ilia Roustemoglou
(Loughborough)
Photo of Falconer Steven
Falconer Steven
(Manchester)
Photo of Jorge Vazquez
Jorge Vazquez
(Exeter)
Photo of nicolas werning
nicolas werning
(Reading)
Photo of Bryan Williams
Bryan Williams
(Liverpool)


Prerequisites


Undergraduate courses on real analysis and partial differential equations(methods courses) will be assumed without explicit mention. Functionalanalysis is more problematic (as applied mathematics students may not havetaken such options) but time constraints prevent assuming no priorknowledge. Probably the best way forward is to present some necessaryfunctional analysis briefly during the lectures and to provide ädditional"notes online and together with careful page references to books covering thematerial in the hope that students who have little or no functional analysiswill wish to learn more in ßelf-study" as a means to coming to a deeperunderstanding of the "theory" of PDEs.

Syllabus


  • Systems of first order pdes and single pdes of higher order, examples from continuum mechanics
  • Symbol of a pde and of systems; characteristics; existence, uniqueness and continuous dependence on the data; well- and ill-posedness.
  • (Brief exposition of necessary functional analysis, e.g. operator theory, distributions, Sobolev spaces).
  • Weak and strong solutions.
  • Maximum principles for elliptic and parabolic pde's, existence of solutions.
  • Linear elliptic pde's, coercivity/energy estimates; Lax-Milgram lemma, Garding's inequality, existence and uniqueness of weak solutions.
  • Evolutionary pde's - abstract parabolic initial value problems, energy methods, uniqueness and existence.
  • Nonlinear elliptic pde's, monotone operators, existence of a weak solution.
  • Systems of hyperbolic equations; Symmetrisable systems; well-posedness.
  • Introduction to semi-group methods.

Bibliography


No bibliography has been specified for this course.

Assessment


There are two assessments.
They are equally weighted.
Assessment 1 was due April 9th.
Assessment 2 is due May 30th.

Assignments


First Assessment

Files:Exam paper
Deadline: Monday 9 April 2012 (982.0 days ago)


Second Assignment

Files:Exam paper
Deadline: Wednesday 30 May 2012 (931.0 days ago)