کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
422000 | 684999 | 2008 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Complexity of Blowup Problems
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
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چکیده انگلیسی
Consider the initial value problem of the first-order ordinary differential equationddtx(t)=f(t,x(t)),x(t0)=x0 where the locally Lipschitz continuous function f:Rl+1âRl with open domain and the initial datum (t0,x0)âRl+1 are given. It is shown that the solution operator producing the maximal “time” interval of existence and the solution on it is computable. Furthermore, the complexity of the blowup problem is studied for functions f defined on the whole space. For each such function f the set Z of initial conditions (t0,x0) for which the positive solution does not blow up in finite time is a Gδ-set. There is even a computable operator determining Z from f. For l⩾2 this upper Gδ-complexity bound is sharp. For l=1 the blowup problem is simpler.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Electronic Notes in Theoretical Computer Science - Volume 221, 25 December 2008, Pages 219-230
Journal: Electronic Notes in Theoretical Computer Science - Volume 221, 25 December 2008, Pages 219-230
نویسندگان
Robert Rettinger, Klaus Weihrauch, Ning Zhong,