"On a proof by Hörmander for the existence of solutions
of parabolic equations"
I will discuss a proof by Hörmander for the existence of solutions of
equations of the form $u_t+f(u)_x=u_{xx}$. The proof is published in
his book "Lectures on Nonlinear Hyperbolic Differential
Equations". The proof does not use advanced theory and is "self-contained".
His proof is for a more general equation of the form
$u_t+ \psi(x,t,u)\cdot \nabla u=\Delta u$, but we will stick to the
simpler equation above. Additional details to the original proof will
be offered.
Helge Holden <holden@math.ntnu.no>
2001-03-15 13:20