 |
|
|
|
|
My research interests include nonlinear partial differential equations and
their applications.
|
|
|
|
Selected Publications
|
|
|
- Integrodifference Models for Persistence in Temporally
Varying Environments, (with Y. Jin (U Alberta) and M. Lewis (U
Alberta)), (2012) in preparation.
- R0-analysis of a spatiotemporal model for a
stream population, (with H. Mckenzie (U Alberta), Y. Jin (U
Alberta), and M. Lewis (U Alberta), SIAM J. Appl. Dyn. Syst (2012), pp. 567-596.
- Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers Equation, (with V. Camacho (HMC '07) and R. Guy (UC Davis), Siam J. Appl. Math., (2008) Vol. 68, pp. 1316-1332.
- As Flat As Possible, SIAM Review, Vol 49, no 3 (2007) pp. 491-507.
- Turing Patterns on Growing Spheres: The Exponential Case (with J. Gjorgjieva), Discrete Contin. Dyn. Syst., (2007), Series A, suppl., p. 436-445. Note: There is an error in the diffusion-driven calculation in this paper as kindly pointed out by Madzvamuse et al. See "Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains, J. Math Biol. (2010)" for an alternate approach to determining the diffusion-driven instability condition.
- Approximations of Continuous Newton's Method: An Extension of Cayley's Problem, (with B. Tennis (HMC '06) and O. Lewis (HMC '05)), Electronic Journal of Differential Equations, 15, (2007), pp. 163-173. See also Magifractificator Home
-
Radial Solutions of Quasilinear Elliptic Differential Equations
(with K. Schmitt), pp. 359-436 in Handbook of Differential Equations, ed. by Canada, Drabek, Fonda; Elsevier, 2004.
-
A Liouville-Gelfand Equation for k-Hessian Operators,
Rocky Mountain J. Math., Vol. 34(2004), No 2, pp. 665-684.
-
The Liouville-Bratu-Gelfand Problem for Radial Operators (with
K. Schmitt),
J. Differential Equations, Vol. 184(2002), No. 1, pp. 283-298.
-
Monotone
Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere
(with A. Belmonte &
A. Jayaraman),
Electron. J. Diff. Eqns., Vol. 2001(2001), No. 62, pp. 1-17.
- A Globalization of the Implicit Function Theorem wth Applications to Nonlinear Elliptic Equations, in Second Summer School in Nonlinear Analysis (Cuernavaca, Morelos, 2000), Amer. Math. Soc., Providence, RI, 2001, pp. 249-272.
- Global Bifurcation Problems Associated with k-Hessian Operators, Topol. Methods Nonlinear Anal., 14 (1999), pp. 81-130.
- Global Bifurcation Problems for Monge-Ampere Operators, In Nonlinear Analysis and its Applications to Differential Eqauations (Lisbon, 1998), Birkhauser, Boston, MA, 2000, pp. 299-309.
|
|
|
| Thesis Students
|
|
|
|
|
- Kate Burgers '11 Finding the Beat: Adaptive Coupled Oscillators
- Sara Gussin '08 Wavelet Sets
- Doug Rizzolo '08 A Fixed Point Search Algorithm for Approximating Solutions of Differential Equations, Graduate Student, UC Berkeley
- James Moore '07 Optimizing Cancer Treatment, Graduate Student, Mathematical Biology, U. of Utah
- Julijana Gjorgjieva '06
Turing Patterns for Spatiotemporal Models with Growth and Curvature, Graduate Student, Cambridge
- Simon Stump '06 Recolonization in the Face of Disaster, Teaching for World Teach in Namibia
- Natalya St. Clair (Scripps '06) Pattern Formation in PDE's
- Owen Lewis '05,
Julia Set Fractal Basins of Attraction and their Numerical Computation, Graduate Student, UC Davis
- Grant Clifford '04,
Representation Theoretical Approach to n-Candidate Voting, Graduate Student, Rutgers
| | Misc. Links
|
|
|
|
|
|
|