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Evgeny Zemskov (Russian Academy of Sciences)
| Speaker: |
Evgeny Zemskov (Russian
Academy of Sciences)
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| Date: |
Wednesday May 18, 2009
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| Title: |
Traveling waves in
piecewise linear reaction-diffusion systems
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Abstract
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The study of wave propagation is
one of the fundamental problems in nonlinear dynamics. Analytical
approaches, which reveal qualitative properties of solutions of the
underlying partial differential equations, deepen our understanding of
experimental
and numerical studies of excitable systems, which are described by
reaction-diffusion equations. However, due to the nonlinearity of the
reaction terms, the theoretical treatment of the problem is
complicated. Various simplifying assumptions are made to avoid
intractable derivations. The nonlinearity is approximated by linear
pieces. Exact solutions of traveling wave type are obtained for the
propagating fronts, pulses and periodic wave-trains, the bifurcation
diagram of the front velocity is determined and the equation of the
growth rate of disturbances is discussed.
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