Jun-Ho Seo

Large-diffusion dynamics for a planar Neumann heat equation with exponential nonlinearity

We study the Neumann problem $u_t-\varepsilon\Delta u=e^u-1-au\ (a>1)$ on a smooth bounded domain $\Omega\subset\mathbb{R}^2$. For the spatially homogeneous problem, $0$ is stable, the positive equilibrium $\xi_a$ is unstable, and solutions starting above $\xi_a$ blow up in finite time. Although finite-time blow-up per...