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Nonhomogeneous Boundary Value Problems for the Korteweg-de Vries Equation on a Bounded Domain

Kramer, Eugene

Abstract Details

2009, PhD, University of Cincinnati, Arts and Sciences : Mathematical Sciences.
The Korteweg-de Vries equation models unidirectional propagation of small finite amplitude long waves in a non-dispersive medium. The well-posedness, that is the existence, uniqueness of the solution, and continuous dependence on data, has been studied on unbounded,periodic, and bounded domains.

This research focuses on an initial and boundary value problem (IBVP) for the Korteweg-de Vries (KdV) equation posed on a bounded interval with general nonhomogeneous boundary conditions. Using Kato smoothing properties of an associated linear problem and the contraction mapping principle, the IBVP is shown to be locally well-posed given several conditions on the parameters for the boundary conditions, in the L²-based Sobolev space Hs(0, 1) for any s≥0.

Bingyu Zhang, PhD (Committee Chair)
H Dumas, PhD (Committee Member)
Anthony Leung, PhD (Committee Member)
Philip Korman, PhD (Committee Member)
98 p.

Recommended Citations

Citations

  • Kramer, E. (2009). Nonhomogeneous Boundary Value Problems for the Korteweg-de Vries Equation on a Bounded Domain [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1258478397

    APA Style (7th edition)

  • Kramer, Eugene. Nonhomogeneous Boundary Value Problems for the Korteweg-de Vries Equation on a Bounded Domain. 2009. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1258478397.

    MLA Style (8th edition)

  • Kramer, Eugene. "Nonhomogeneous Boundary Value Problems for the Korteweg-de Vries Equation on a Bounded Domain." Doctoral dissertation, University of Cincinnati, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1258478397

    Chicago Manual of Style (17th edition)