کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4617735 1339388 2012 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Existence of the global solution for the parabolic Monge–Ampère equations on compact Riemannian manifolds
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Existence of the global solution for the parabolic Monge–Ampère equations on compact Riemannian manifolds
چکیده انگلیسی

On a compact Riemannian manifold (M,g)(M,g), we consider the existence and nonexistence of global solutions for the parabolic Monge–Ampère equationequation(⁎){∂∂tφ=log(det(g+Hessφ)detg)−λφp−f(x),φ(x,0)=φ0(x). Here p>1p>1 and λ   are real parameters. −f,φ0:M→(0,+∞)−f,φ0:M→(0,+∞) are smooth functions on M  . If λ>0λ>0, then the solution φ of (⁎) exists for all times t   and φt=φ(⋅,t)φt=φ(⋅,t) converges exponentially towards a solution φ∞φ∞ of its stationary equation as t→∞t→∞. In the case of λ<0λ<0, it does not have the global solution of (⁎). Thus we obtain the nonexistence of the positive solution for the stationary equation of (⁎).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 389, Issue 1, 1 May 2012, Pages 597–607
نویسندگان
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