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- Bernard Deconinck, Beatrice Pelloni, Natalie E. Sheils
- Proceedings. Mathematical, physical, andâ€¦
- 2014

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. Theâ€¦ (More)

- Joseph P. Previte, Natalie E. Sheils, Kathleen A. Hoffman, Tim Kiemel, Eric D. Tytell
- Journal of mathematical biology
- 2011

In the vertebrate spinal cord, a neural circuit called the central pattern generator produces the basic locomotory rhythm. Short and long distance intersegmental connections serve to maintainâ€¦ (More)

- Natalie E. Sheils, Bernard Deconinck
- Appl. Math. Lett.
- 2014

The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicitâ€¦ (More)

The interface problem for the linear Korteweg-de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location ofâ€¦ (More)

u j : RN Ã— R â†’ C, Ïˆ j0 : RN â†’ C for j = 1, 2, . . . , m and ajk = akj are positive real numbers. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of aâ€¦ (More)

In the vertebrate spinal cord, a neural circuit called the central pattern generator produces the basic locomotory rhythm. Short and long distance intersegmental connections serve to maintainâ€¦ (More)

In the vertebrate spinal cord, a neural circuit called the central pattern generator produces the basic locomotory rhythm. Short and long distance intersegmental connections serve to maintainâ€¦ (More)

A map from the initial conditions to the values of the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with nâ€¦ (More)

In this manuscript, we consider the Cauchy problem for a SchrÃ¶dinger system with power-type nonlinearities ï£²ï£³ i âˆ‚ âˆ‚tuj +4uj + âˆ‘m k=1 ajk|uk||uj|uj = 0, uj(x, 0) = Ïˆj0(x), where uj : R Ã— R â†’ C, Ïˆj0 :â€¦ (More)

The original Lamb system was introduced by Horace Lamb in 1900, [13], as a simple model for the phenomenon of radiation damping experienced by a vibrating body in an energy conducting medium.â€¦ (More)