5 problems

Let $p>1$ and let denote the diffusive Hamilton–Jacobi problem studied in the source. An entire solution is a solution defined for all $t\in\mathbb{R}$; it is nonstationary if it d…

Let $mathbb R^2$ be generated by repeated even extension of solutions from fundamental domains, and consider an isosceles right triangle and the corresponding square. Triangle-squa…

Let $(u,v)$ be an entire solution of the Keller–Segel system on $\mathbb{R}^2\times\mathbb{R}$, meaning that $u$ and $\nabla v$ are smooth and satisfy the system, with the second e…

Let $u$ be an entire solution of the bistable reaction diffusion equation referred to as, and let the asymptotic stable states of this equation be the stable states defined in the…

Consider the elliptic system … in Euclidean space, together with the higher-dimensional constructions and properties discussed for this system and for the Allen–Cahn equation. High…