PDE seminar: Complex-valued heat equation with quadratic nonlinearity

2012-4-16 16:30 - 2012-4-16 17:30
Faculty of Science Building #3 Room 202
Masahiko Shimojo (Hokkaido Univ.)
We consider the Cauchy problem for a system of parabolic equations
which is derived from a complex-valued equation with a quadratic nonlinearity.

Our equation has a strong relation with the viscous Constantin-Lax-Majda equation, which is
a one dimensional model for the vorticity equation.

First we discuss a criterion that the solution exists globally in time and
converges to the trivial steady state. Next, on the one dimensional space,
we provide some solutions with nontrivial imaginary part that blow up simultaneously.

This is the joint work with H. Ninomiya, E. Yanagida and J.S. Guo.