On inertial manifolds for reaction-diffusion equations on genuinely high-dimensional thin domains
Martino Prizzi, Krzysztof P. Rybakowski · Studia Mathematica · 2003
We study a family of semilinear reaction-diffusion equations on spatial domains ${\mit \Omega }_\varepsilon $, $\varepsilon >0$, in ${\mathbb R}^ l $ lying close to a $k$-dimensional submanifold ${{\cal M}}$ of ${\mathbb R}^ l $. As $\varepsilon \to 0^+$,