ترغب بنشر مسار تعليمي؟ اضغط هنا

Asymptotic profiles of solutions to convection-diffusion equations

191   0   0.0 ( 0 )
 نشر من قبل Said Benachour
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English
 تأليف Said Benachour




اسأل ChatGPT حول البحث

The large time behavior of zero mass solutions to the Cauchy problem for a convection-diffusion equation. We provide conditions on the size and shape of the initial datum such that the large time asymptotics of solutions is given either by the derivative of the Guass-Weierstrass kernel or by a self-similar solution or by a hyperbolic N-wave



قيم البحث

اقرأ أيضاً

201 - Said Benachour 2007
The large time behavior of solutions to Cauchy problem for viscous Hamilton-Jacobi equation is classified. The large time asymptotics are given by very singular self-similar solutions on one hand and by self-similar viscosity solutions on the other hand
We study extinction profiles of solutions to fast diffusion equations with some initial data in the Marcinkiewicz space. The extinction profiles will be the singular solutions of their stationary equations.
116 - Hironori Michihisa 2017
In this paper we obtain higher order asymptotic profilles of solutions to the Cauchy problem of the linear damped wave equation in $textbf{R}^n$ begin{equation*} u_{tt}-Delta u+u_t=0, qquad u(0,x)=u_0(x), quad u_t(0,x)=u_1(x), end{equation*} where $n intextbf{N}$ and $u_0$, $u_1in L^2(textbf{R}^n)$. Established hyperbolic part of asymptotic expansion seems to be new in the sense that the order of the expansion of the hyperbolic part depends on the spatial dimension.
In this paper we obtain the precise description of the asymptotic behavior of the solution $u$ of $$ partial_t u+(-Delta)^{frac{theta}{2}}u=0quadmbox{in}quad{bf R}^Ntimes(0,infty), qquad u(x,0)=varphi(x)quadmbox{in}quad{bf R}^N, $$ where $0<theta<2$ and $varphiin L_K:=L^1({bf R}^N,,(1+|x|)^K,dx)$ with $Kge 0$. Furthermore, we develop the arguments in [15] and [18] and establish a method to obtain the asymptotic expansions of the solutions to a nonlinear fractional diffusion equation $$ partial_t u+(-Delta)^{frac{theta}{2}}u=|u|^{p-1}uquadmbox{in}quad{bf R}^Ntimes(0,infty), $$ where $0<theta<2$ and $p>1+theta/N$.
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to zero or to infinity.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا