Applied Analysis

Seminar information archive ~05/21Next seminarFuture seminars 05/22~

Date, time & place Thursday 16:00 - 17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

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16:00-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Eiji Yanagida (Tokyo Institute of Technology)
Sign-changing solutions for a one-dimensional semilinear parabolic problem (Japanese)
[ Abstract ]
This talk is concerned with a nonlinear parabolic equation on a bounded interval with the homogeneous Dirichlet or Neumann boundary condition. Under rather general conditions on the nonlinearity, we consider the blow-up and global existence of sign-changing solutions. It is shown that there exists a nonnegative integer $k$ such that the solution blows up in finite time if the initial value changes its sign at most $k$ times, whereas there exists a stationary solution with more than $k$ zeros. The proof is based on an intersection number argument combined with a topological method.