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GCOE Seminars
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
2014/03/06
16:20-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)
M. Cristofol (Aix-Marseille Univ.)
New kind of observations in an inverse parabolic problem (ENGLISH)
M. Cristofol (Aix-Marseille Univ.)
New kind of observations in an inverse parabolic problem (ENGLISH)
[ Abstract ]
In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.
In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.
