Now showing items 1-8 of 8

    • Entire Solutions to Dirichlet Type Problems 

      Sitar, Scott (University of Waterloo, 2007-08-02)
      In this thesis, we examined some Dirichlet type problems of the form: \begin{eqnarray*} \triangle u & = & 0\ {\rm in\ } \mathbb{R}^n \\ u & = & f\ {\rm on\ } \psi = 0, \end{eqnarray*} and we were particularly ...
    • A geometric investigation of non-regular separation applied to the bi-Helmholtz equation & its connection to symmetry operators 

      Jayyusi, Basel (University of Waterloo, 2024-05-23)
      The theory of non-regular separation is examined in its geometric form and applied to the bi-Helmholtz equation in the flat coordinate systems in 2-dimensions. It is shown that the bi-Helmholtz equation does not admit ...
    • Late-lumping backstepping control of partial differential equations 

      Auriol, Jean; Morris, Kirsten; Di Meglio, Florent (Elsevier, 2019-02)
      We consider in this paper three different partial differential equations (PDEs) that can be exponentially stabilized using backstepping controllers. For implementation, a finite-dimensional controller is generally needed. ...
    • Long-time behaviour of a coupled PDE model of high intensity focused ultrasound heating of biological tissue 

      Murley, June (University of Waterloo, 2021-11-11)
      High Intensity Focused Ultrasound (HIFU) has emerged as a novel therapeutic modality, for the treatment of various cancers, that is gaining significant traction in clinical oncology. It is a cancer therapy that avoids many ...
    • Mathematical Modeling of C elegans L1 aggregation 

      Avery, Leon (University of Waterloo, 2020-01-16)
      First-stage larvae (L1s) of the nematode Caenorhabditis elegans aggregate after starvation. I develop a mathematical model of this behavior based on the classic Keller-Segel model. In the Keller-Segel model, organisms ...
    • Microcolony Dynamics: Motion from Growth, Order, and Incompressibility 

      Smith-Roberge, Julien (University of Waterloo, 2023-04-27)
      Rod-shaped bacteria such as E. coli reproduce by expanding along their long axis and splitting into pairs of daughter cells. If conditions are favourable for growth, they will continue in this way, doubling repeatedly until ...
    • Stability and Well-posedness of a Nonlinear Railway Track Model 

      Edalatzadeh, M. Sajjad; Morris, Kirsten (Institute of Electrical and Electronics Engineers, 2018-06-22)
      Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions ...
    • The two-space homogenization method 

      Murley, Jonathan (University of Waterloo, 2012-10-04)
      In this thesis, we consider the two-space homogenization method, which produces macroscopic expressions out of descriptions of the behaviour of the microstructure. Specifically, we focus on its application to poroelastic ...


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