758Tsikkou

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Spring 2016

Course Information

Description: Theory of Partial Differential Equations 2

Instructor: Charis Tsikkou. Email

Class Schedule: Tuesdays, Thursdays 02:30-03:45 PM in Armstrong Hall 203

Office Hours: Tuesdays 04:00-05:00 PM, Thursdays 01:00-02:00 PM, and by appointment, in Armstrong Hall 405

Info Sheet containing more or less the stuff on this webpage.

Textbook

Textbook:

Lawrence C. Evans, Partial Differential Equations: Second Edition (Graduate Studies in Mathematics)

Errata for “Partial Differential Equations”, AMS Press, Second Edition by Lawrence C. Evans

Alternative Textbook:

Emmanuele DiBenedetto, Partial Differential Equations: Second Edition (Cornerstones)

Gerald B. Folland, Introduction to Partial Differential Equations: Second Edition

Fritz John, Partial Differential Equations (Applied Mathematical Sciences)

Robert C. McOwen, Partial Differential Equations: Methods and Applications (2nd Edition)

Michael Renardy and Robert C. Rogers, An Introduction to Partial Differential Equations (Texts in Applied Mathematics)

Jeffrey Rauch, Partial Differential Equations (Graduate Texts in Mathematics)

Walter Strauss, Partial Differential Equations: An Introduction

Evaluation

Grading scheme

  • 35% Final exam
  • 25% Midterm exam
  • 40% Homework Assignments
  • Letter grades will be assigned according to the scheme
A 90-100% | B 80-90% | C 70-80% | D 60-70% | F 0-60%

Homework

  • Homework will be assigned once every three weeks, and due two weeks later (please see the course schedule below for exact dates).
  • Homework will always be collected at the beginning of the class.
  • Late turn-ins will not be accepted.

Midterm Exam

  • There will be one take-home exam, posted: Thursday, March 10, due: Tuesday, March 15.
  • No make-up exam will be given.

Final Exam

  • Due: Thursday, May 5.
  • Final is cumulative.

Course Schedule (subject to changes)

Date Topic Resources HW
Tuesday, Jan 12 Introduction to Conservation Laws; Shocks, Entropy Condition 3.4.1
Thursday, Jan 14 Examples; Shock and Rarefaction Waves; Entropy Solution 3.4.1 - 3.4.3
Tuesday, Jan 19 Riemann's Problem; Separation of Variables; Examples 3.4.4, 4.1.1
Thursday, Jan 21 Similarity Solutions; Plane and Traveling Waves; Solitons 4.2.1 HW 1 posted, solutions
Tuesday, Jan 26 Examples 4.2.1
Thursday, Jan 28 Similarity Under Scaling; Fourier Transform 4.2.2, 4.3.1
Tuesday, Feb 2 Plancherel's Theorem; Properties 4.3.1
Thursday, Feb 4 Examples 4.3.1
Tuesday, Feb 9 Laplace Transform; Examples; Cole-Hopf Transformation 4.3.3, 4.4.1
Thursday, Feb 11 Examples; Holder Spaces; Weak Derivatives 4.4.1, 5.1, 5.2.1 HW 2 posted, solutions
Tuesday, Feb 16 Sobolev Spaces; Definitions ; Examples 5.2.2
Thursday, Feb 18 Elementary Properties 5.2.3
Tuesday, Feb 23 Sobolev Spaces as Function Spaces 5.2.3
Thursday, Feb 25 Local Approximation by Smooth Functions 5.3.1
Tuesday, Mar 1 Global Approximation by Smooth Functions 5.3.2
Thursday, Mar 3 Global Approximation by Functions Smooth up to the Boundary 5.3.3 HW 3 posted, solutions
Tuesday, Mar 8 Extensions 5.4
Thursday, Mar 10 Extension Theorem 5.4 Midterm Exam posted, solutions
Tuesday, Mar 15 Problem Solving
Thursday, Mar 17 Traces 5.5
Tuesday, Mar 22 No Class (Spring Recess)
Thursday, Mar 24 No Class (Spring Recess) HW 4 posted, solutions
Tuesday, Mar 29 Traces; Sobolev Inequalities 5.5, 5.6.1
Thursday, Mar 31 Gagliardo-Nirenberg-Sobolev Inequality 5.6.1
Tuesday, Apr 5 Estimates for W 1,p and W0 1,p, p < n 5.6.1
Thursday, Apr 7 Morrey's Inequality 5.6.2
Tuesday, Apr 12 Estimates for W 1,p, n < p 5.6.2
Thursday, Apr 14 General Sobolev Inequalities 5.6.3 HW 5 posted, solutions
Tuesday, Apr 19 Rellich-Kondrachov Compactness Theorem 5.7
Thursday, Apr 21 Hardy's Inequality 5.8.4
Tuesday, Apr 26 The Dual space H -1; Second-Order Elliptic Equations 5.9.1, 6.1.1
Thursday, Apr 28 Weak Solutions; Lax-Milgram Theorem; Energy Estimates 6.1.2 - 6.2.2
Thursday, May 5 Final Exam Final Exam posted, solutions

Inclusivity statement

The West Virginia University community is committed to creating and fostering a positive learning and working environment based on open communication, mutual respect, and inclusion. If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Accessibility Services (293-6700). For more information on West Virginia University's Diversity, Equity, and Inclusion initiatives, please see http://diversity.wvu.edu.

Accessibility Needs

If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Disability Services (304-293-6700).