Seminar 22.2.2018: Eiji Yanagida

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 22.2.2018: Eiji Yanagida

Postby quittner » Mon Feb 12, 2018 11:31 am

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 22.2.2018 at 14:00 Lecture room M-223

Eiji Yanagida (Tokyo Institute of Technology):
Blow-up of sign-changing solutions for a one-dimensional semilinear parabolic equation

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 inhomogeneous. 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 result 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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