کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4612364 | 1338679 | 2006 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Cross-shaped and degenerate singularities in an unstable elliptic free boundary problem
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We investigate singular and degenerate behavior of solutions of the unstable free boundary problemΔu=−χ{u>0}.Δu=−χ{u>0}. First, we construct a solution that is not of class C1,1C1,1 and whose free boundary consists of four arcs meeting in a cross-shaped singularity. This solution is completely unstable/repulsive from above and below which would make it hard to get by the usual methods, and even numerics is nontrivial. We also show existence of a degenerate solution. This answers two of the open questions in the paper [R. Monneau, G.S. Weiss, An unstable elliptic free boundary problem arising in solid combustion, http://arxiv.org/abs/math.AP/0507315, submitted for publication].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 228, Issue 2, 15 September 2006, Pages 633–640
Journal: Journal of Differential Equations - Volume 228, Issue 2, 15 September 2006, Pages 633–640
نویسندگان
J. Andersson, G.S. Weiss,