Seminar on PDE
主講者: | Eiji Yanagida (Tokyo Institute of Technology) |
講題: | Blow-up of sign-changing solutions for a one-dimensional semilinear parabolic equation |
時間: | 2018-01-30 (Tue.) 10:00 - 11:00 |
地點: | 數學所 722 研討室 (台大院區) |
Abstract: | This talk is concerned with a nonlinear parabolic equation on a bounded interval with the Dirichlet or Neumann boundary condition, where the nonlinearity is superlinear and spatially inhomogenous. 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. This results is an extension of Mizoguchi-Yanagida (1996) which dealt with an odd and spatially homogenous nonlinearity. The proof is based on an intersection number argument combined with a topological method. |
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