کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665542 1633816 2015 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Oscillation-induced blow-up to the modified Camassa–Holm equation with linear dispersion
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Oscillation-induced blow-up to the modified Camassa–Holm equation with linear dispersion
چکیده انگلیسی


• Formation of singularities to an integrable model in shallow-water waves is studied.
• A blow-up mechanism to the model with varying linear dispersion is provided.
• Blow-up is induced by a slow oscillation of initial data.

In this paper, we provide a blow-up mechanism to the modified Camassa–Holm equation with varying linear dispersion. We first consider the case when linear dispersion is absent and derive a finite-time blow-up result with an initial data having a region of mild oscillation. A key feature of the analysis is the development of the Burgers-type inequalities with focusing property on characteristics, which can be deduced from tracing the ratio between solution and its gradient. Using the continuity and monotonicity of the solutions, we then extend this blow-up criterion to the case of negative linear dispersion, and determine that the finite time blow-up can still occur if the initial momentum density is bounded below by the magnitude of the linear dispersion and the initial datum has a local mild-oscillation region. Finally, we demonstrate that in the case of non-negative linear dispersion the formation of singularities can be induced by an initial datum with a sufficiently steep profile. In contrast to the Camassa–Holm equation with linear dispersion, the effect of linear dispersion of the modified Camassa–Holm equation on the blow-up phenomena is rather delicate.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 272, 26 February 2015, Pages 225–251
نویسندگان
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