3 problems

Let $\mathcal{H}$ be the space of heteroclinic orbits of the semilinear parabolic equation, and let $Y_\lambda$ denote the ambient space in which these orbits are considered. Ident…

Generic simplicity conjecture. There is a generic subset (a Baire subset) of choices for $\phi$ in $$ such that, if $u$ is a heteroclinic orbit, all of the eigenvalues of $H(t)$ ar…

Let $u$ be an eternal solution of the semilinear parabolic equation \, with coefficients $a_i$ that decay sufficiently fast as $|x|\to\infty$. Heteroclinic-orbit conjecture. All…