Speaker :
 Eiji Yanagida (Tokyo Institute of Technology) 
Title :

Blowup of signchanging solutions for a onedimensional semilinear parabolic equation 
Time :
 20180130 (Tue) 10:00  11:00 
Place : 
Seminar Room 722, Institute of Mathematics (NTU Campus) 
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 blowup and global existence of signchanging 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 MizoguchiYanagida (1996) which dealt with an odd and spatially homogenous nonlinearity. The proof is based on an intersection number argument combined with a topological method. 