کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5774192 1413549 2017 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations
ترجمه فارسی عنوان
یک شرط لازم و کافی برای منحصر به فرد راه حل نهایی در معادلات نیمهلیا پارابولی
کلمات کلیدی
نیمه خطی، پارابولیک، اسگود، غیر منحصر به فرد، منحصر به فرد، راه حل پایین،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
In their (1968) paper Fujita and Watanabe considered the issue of uniqueness of the trivial solution of semilinear parabolic equations with respect to the class of bounded, non-negative solutions. In particular they showed that if the underlying ODE has non-unique solutions (as characterised via an Osgood-type condition) and the nonlinearity f satisfies a concavity condition, then the parabolic PDE also inherits the non-uniqueness property. This concavity assumption has remained in place either implicitly or explicitly in all subsequent work in the literature relating to this and other, similar, non-uniqueness phenomena in parabolic equations. In this paper we provide an elementary proof of non-uniqueness for the PDE without any such concavity assumption on f. An important consequence of our result is that uniqueness of the trivial solution of the PDE is equivalent to uniqueness of the trivial solution of the corresponding ODE, which in turn is known to be equivalent to an Osgood-type integral condition on f.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 262, Issue 10, 15 May 2017, Pages 4979-4987
نویسندگان
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