کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4610406 1338561 2014 34 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow
ترجمه فارسی عنوان
اثبات عددی ثبات امواج رول در دامنه کوچک دامنه برای جریان فیلم نازک شیب دار
کلمات کلیدی
اولیه، 35، ثانویه 65
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV–KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar–Nepomnyashchy and Johnson–Noble–Rodrigues–Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 257, Issue 8, 15 October 2014, Pages 2950–2983
نویسندگان
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