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NEW ASYMPTOTIC METHODS IN THE STUDY OF ANALYTIC DIFFERENTIAL AND DYNAMICAL SYSTEMS
Park, Hyejin

2014, Doctor of Philosophy, Ohio State University, Mathematics.
In the first part of the dissertation, we prove Borel summability in nonsingular directions of heatlike equation u_t = a(z)u_zz in the complex domain where a(z) is a quartic polynomial and the initial condition is analytic. In the special case a(z) = z we obtain the detailed resurgent structure; even in such a simple case, the structure of the singular manifolds is quite intricate. In the second part of the disseration, we provide mainly two applications of transseries and Borel summation to interesting problems such as nonelementarity of a function, and analytic factorizability of a linear operator. In the third part, we consider the dynamical system arising in submonolayer deposition model, and analyze the asymptotic behavior of the solution as t goes to infinity.
Ovidiu Costin (Advisor)
Rodica Costin (Committee Member)
Yuji Kodama (Committee Member)
78 p.

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Park, H. (2014). NEW ASYMPTOTIC METHODS IN THE STUDY OF ANALYTIC DIFFERENTIAL AND DYNAMICAL SYSTEMS. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Park, Hyejin. "NEW ASYMPTOTIC METHODS IN THE STUDY OF ANALYTIC DIFFERENTIAL AND DYNAMICAL SYSTEMS." Electronic Thesis or Dissertation. Ohio State University, 2014. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Park, Hyejin "NEW ASYMPTOTIC METHODS IN THE STUDY OF ANALYTIC DIFFERENTIAL AND DYNAMICAL SYSTEMS." Electronic Thesis or Dissertation. Ohio State University, 2014. https://etd.ohiolink.edu/

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