کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898852 | 1631502 | 2018 | 42 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions
ترجمه فارسی عنوان
در مورد هذلولی و جورجی خوب بودن. قسمت دوم: گذارهای اسکالر یا دگرگون شده
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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 GÏ to L2, with 0<Ï<Ï0, the limiting Gevrey index Ï0 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.].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 8, 15 April 2018, Pages 5221-5262
Journal: Journal of Differential Equations - Volume 264, Issue 8, 15 April 2018, Pages 5221-5262
نویسندگان
Baptiste Morisse,