MATH 674, PARTIAL DIFFERENTIAL EQUATIONS II 

Spring 2019

Instructor: Konstantina Trivisa:

Office: 3307 Mathematics Bldg 

Phone: (301) 405-6865

Office Hours: (Spring 2019) Tu, Th 9:00 - 10:15 or by appointment. 

Email: trivisa@math.umd.edu 

An introduction to the theory of  Hyperbolic Systems of Conservation Laws. Modern methods for PDEs: distributions, functional analysis, Sobolev spaces,

bounded and compact operators in Hilbert spaces. Mathematical theory of compressible fluids.

Prerequisites:
MATH 411 or equivalent. 

Main Text:

• Lawrence C. Evans, Partial Differential Equations
  The syllabus of Math 674/AMSC 674 consists of the core material in Chapters 5 and 6 and of selected topics from Chapters 11 and 7-9. 

Further reading 

Elliptic partial differential equations of second order by D. Gilbarg and N.  Trudinger

Hyperbolic conservation laws in continuum physics by Constantine M. Dafermos

On the dynamics of compressible fluids by E. Feireisl

Class Times: Tuesday and Thursday: 11:00am - 12:15pm. 

Location: MTH 0403

• 
  COURSE OUTLINE
• Hyperbolic Systems of Conservation Laws
• Distributions
• Boundary value problems for elliptic partial differential equations via operator-theoretic methods 
• Hilbert spaces of functions 
• Duality, weak convergence 
• Sobolev spaces 
• Spectral theory of compact operators 
• Mathematical theory of compressible fluids
• 
  

Grading (approximate):

• Homework: 40% 
• Midterm : 30% 
• Final: 30% 

Assignments: Homeworks will be assigned and collected.

• HOMEWORK
  homework1.pdf, homework2.pdf, homework3.pdf
  homework4.pdf homework5.pdf