On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

the effect of traffic density on the accident externality from driving the case study of tehran

در این پژوهش به بررسی اثر افزایش ترافیک بر روی تعداد تصادفات پرداخته شده است. به این منظور 30 تقاطع در شهر تهران بطور تصادفی انتخاب گردید و تعداد تصادفات ماهیانه در این تقاطعات در طول سالهای 89-90 از سازمان کنترل ترافیک شهر تهران استخراج گردید و با استفاده از مدل داده های تابلویی و نرم افزار eviews مدل خطی و درجه دوم تخمین زده شد و در نهایت این نتیجه حاصل شد که تقاطعات پر ترافیک تر تعداد تصادفا...

On the Asymptotic Stabilty of Stationary Solutions of the Inviscid Incompressible Porous Medium Equation

We study the stability of stationary solutions of the 2D inviscid incompressible porous medium equation (IPM). We show that solutions which are near certain stable stationary solutions must converge as t → ∞ to a stationary solution of the IPM equation. It turns out that linearizing the IPM equation about certain stable stationary solutions gives a non-local partial damping mechanism. On the to...

Asymptotic L1-decay of Solutions of the Porous Medium Equation to Self-similarity

We consider the flow of gas in an N-dimensional porous medium with initial density v0(x) ≥ 0. The density v(x, t) then satisfies the nonlinear degenerate parabolic equation vt = ∆vm where m > 1 is a physical constant. Assuming that ∫ (1 + |x|2)v0(x)dx < ∞, we prove that v(x, t) behaves asymptotically, as t → ∞, like the Barenblatt-Pattle solution V(|x|, t). We prove that the L1-distance decays ...

Regularity of weak solutions of the Cauchy problem to a fractional porous medium equation

This paper concerns the regularity of the weak solutions of the Cauchy problem to a fractional porous medium equation with a forcing term. In the recent work (Fan et al. in Comput. Math. Appl. 67:145-150, 2014), the authors established the existence of the weak solution and the uniqueness of the weak energy solution. In this paper, we show that the every nonnegative bounded weak energy solution...

A Very Singular Solution for the Dual Porous Medium Equation and the Asymptotic Behaviour of General Solutions