Abstract
AbstractWe consider high‐order non‐linear hyperbolic equations that are small perturbations of an equation with constant coefficients. It is assumed that the unperturbed equation has a characteristic polynomial whose roots with respect to the variable dual to time are outside an open strip containing the imaginary axis. We establish the property of exponential dichotomy for the equation in question. Under the additional condition that the roots of the characteristic polynomial belong to the left half‐plane we prove that the zero solution is asymptotically stable as t → + ∞.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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