کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7222770 | 1470498 | 2014 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density
ترجمه فارسی عنوان
رفتار بزرگ زمان برای یک معادله متوسط متخلخل در یک محیط غیرمجاز با تراکم بحرانی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی (عمومی)
چکیده انگلیسی
We study the large time behavior of solutions to the Cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density |x|â2âtu=Îum,inRNÃ(0,â), where m>1 and Nâ¥3, with nonnegative initial condition u(x,0)=u0(x)â¥0. The asymptotic behavior proves to have some interesting and striking properties. We show that there are different asymptotic profiles for the solutions, depending on whether the continuous initial data u0 vanishes at x=0 or not. Moreover, when u0(0)=0, we show the convergence towards a peak-type profile presenting a jump discontinuity, coming from an interesting asymptotic simplification to a conservation law, while when u0(0)>0, the limit profile remains continuous. These phenomena illustrate the strong effect of the singularity at x=0. We improve the time scale of the convergence in sets avoiding the singularity. On the way, we also study the large-time behavior for a porous medium equation with convection which is interesting for itself.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 102, June 2014, Pages 226-241
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 102, June 2014, Pages 226-241
نویسندگان
Razvan Gabriel Iagar, Ariel Sánchez,