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Asymptotic behavior of singular solutions for a semilinear parabolic equation

Tuesday, September 25, 2012 - 2:00pm - 2:50pm
Keller 3-180
Eiji Yanagida (Tokyo Institute of Technology)
We consider singular solutions of a parabolic partial differential
equation with power nonlinearity. It is known that in some range of
parameters, this equation has a family of singular steady states with
ordered structure. Our concern is the existence of
time-dependent singular solutions and their asymptotic behavior,
the convergence of solutions to singular steady states. Our method is
based on the analysis of a related linear equation with a singular
coefficient and the comparison principle. This is a joint work with
Masaki Hoshino and Shota Sato.
MSC Code: 
35K58