Abstract
In this paper we prove the global existence, uniqueness, optimal large time decay rates, and uniform gain of analyticity for the exponential PDE $h_t=\Delta e^{-\Delta h}$ in the whole space $\mathbb{R}^d_x$. We assume the initial data is of medium size in the critical Wiener algebra $\Delta h \in A(\mathbb{R}^d)$. This exponential PDE was derived in (Krug, Dobbs, and Majaniemi in 1995) and more recently in (Marzuola and Weare 2013).
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More From: Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications
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