Essential spectrum of elliptic systems of pseudo-differential operators on $L^2({\mathbb{R}}^N)\oplus L^2({\mathbb{R}}^N)$

Abstract

Inspired by a result of Wong (Commun. Partial Differ. Equ. 13(10):1209-1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order systems of pseudo-differential operators on $L^2({\mathbb{R}}^N)\oplus L^2({\mathbb{R}}^N)$ that are uniformly Douglis-Nirenberg elliptic with positive-order diagonal entries. We apply our result to a problem arising in the dynamics of falling liquid films.

arXiv comment15 pages, 2 figures. To appear in J. Pseudo-Differ. Oper. Appl