دانلود مقاله ISI انگلیسی شماره 161540
ترجمه فارسی عنوان مقاله

در مورد هذلولی و جورجی خوب بودن. قسمت دوم: گذارهای اسکالر یا دگرگون شده

عنوان انگلیسی
On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions
کد مقاله سال انتشار تعداد صفحات مقاله انگلیسی
161540 2018 42 صفحه PDF
منبع

Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : Journal of Differential Equations, Volume 264, Issue 8, 15 April 2018, Pages 5221-5262

پیش نمایش مقاله
پیش نمایش مقاله  در مورد هذلولی و جورجی خوب بودن. قسمت دوم: گذارهای اسکالر یا دگرگون شده

چکیده انگلیسی

For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, we prove a strong Hadamard instability for the associated Cauchy problem, namely an instantaneous defect of Hölder continuity of the flow from Gσ to L2, with 0<σ<σ0, the limiting Gevrey index σ0 depending on the nature of the transition. We restrict here to scalar transitions, and non-scalar transitions in which the boundary of the hyperbolic zone satisfies a flatness condition. As in our previous work for initially elliptic Cauchy problems [B. Morisse, On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, arXiv:1611.07225], the instability follows from a long-time Cauchy–Kovalevskaya construction for highly oscillating solutions. This extends recent work of N. Lerner, T. Nguyen, and B. Texier [The onset of instability in first-order systems, to appear in J. Eur. Math. Soc.].