9 problems

Assume the invasion property, Hypothesis … d{mathcal{H}}(U,Urho)<+infty … . Let $\Omega(u)$ be the omega-limit set of $u$ under time translations. De Giorgi type conjecture. Every…

Palis's conjecture. The property that a vector field has a large set of trajectories going to its attractors holds for a dense set of vector fields on any compact manifold.

Let $M$ be a manifold equipped with a differentially positive system, let $x\in M$, and denote by $\omega(x)$ the $\omega$-limit set of the trajectory through $x$. Forni–Sepulchre'…

Chain-recurrent shock-merger conjecture. In this example, the omega-limit set consists of the shock merger itself and the family of steady shocks with smaller amplitude; together t…

Exact omega-limit-set conjecture. For this initial datum, $\omega_0(u_0)$ is equal to the right-hand side of.

Realizability conjecture. For any probability measure $\mu$ on $[\alpha,\beta]$, there exist initial data $u_0\in L^\infty(\mathbb{R})$ satisfying such that $\omega(u_0)$ contains…

Let $V\in\tilde{\mathcal V}^-$ and let $\frak{f}(V)=(a_{ki})$. For ${\mathbf{x}}\in S$, write $\operatorname{supp}({\mathbf{x}})$ for its support, let ${\mathbf e}_j$ denote the…

Let $u: \mathbb{R} \times \mathbb{R}_+ \to \mathbb{R}$ solve the parabolic equation with initial data $u_0$ satisfying … where $(b_n)_{n\in\mathbb{N}}$ is strictly increasing,…

Let $T:[0,1]\rightarrow[0,1]$ be a tent map with shadowing. A set $L\binom{}{}$?