## 応用解析セミナー

開催情報 木曜日　16:00～17:30　数理科学研究科棟(駒場) 002号室 石毛 和弘

### 2018年05月24日(木)

16:00-17:30   数理科学研究科棟(駒場) 128号室

Sign-changing solutions for a one-dimensional semilinear parabolic problem (Japanese)
[ 講演概要 ]
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.