Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


akron1302552445.pdf (293.66 KB)

ETD Abstract Container

Abstract Header

Uniqueness of Entropy Solutions to Hyperbolic-Parabolic Conservation Laws

Diep, My Tieu
http://rave.ohiolink.edu/etdc/view?acc_num=akron1302552445

Abstract Details

2011, Master of Science, University of Akron, Applied Mathematics.
We consider an initial value problem for the hyperbolic-parabolic equation: u_t + [F(t, x, u)]_x = e u_xx in QT := R x (0, T), u(·, 0)= u_0 in R. Here the flux function has the form F(t, x, u) = K(x)f(u), where f(u) and K(x) are scalar functions. Our purpose is to prove the uniqueness result for entropy solutions of the problem which is of interest in fluid and statistical mechanics. It is known that if K(x)in W_{loc}^{1,1}(R) and f(u) is locally Lipschitz, then the equation has a unique entropy solution. In this thesis we are able to show the uniqueness for entropy solutions of the equation under a much weaker condition: K(x) has locally bounded variation and f(u) is continuous. Our result is useful because in some applications the flux function f(u) is only continuous. We in fact establish a L1-contraction principle for entropy solutions from which one can deduce the uniqueness as a particular consequence.
Truyen Nguyen, Dr. (Advisor)
Dmitry Golovaty, Dr. (Committee Member)
J. Patrick Wilbur, Dr. (Committee Member)
69 p.
Applied Mathematics
entropy solution; uniqueness; conservation law; hyperbolic-parabolic.

Recommended Citations

Citations

  • Diep, M. T. (2011). Uniqueness of Entropy Solutions to Hyperbolic-Parabolic Conservation Laws [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302552445

    APA Style (7th edition)

  • Diep, My. Uniqueness of Entropy Solutions to Hyperbolic-Parabolic Conservation Laws. 2011. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1302552445.

    MLA Style (8th edition)

  • Diep, My. "Uniqueness of Entropy Solutions to Hyperbolic-Parabolic Conservation Laws." Master's thesis, University of Akron, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302552445

    Chicago Manual of Style (17th edition)

akron1302552445
538
© 2011, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.