ﻻ يوجد ملخص باللغة العربية
We prove the convergence of the solutions $u_{m,p}$ of the equation $u_t+(u^m)_x=-u^p$ in $Rtimes (0,infty)$, $u(x,0)=u_0(x)ge 0$ in $R$, as $mtoinfty$ for any $p>1$ and $u_0in L^1(R)cap L^{infty}(R)$ or as $ptoinfty$ for any $m>1$ and $u_0in L^{infty}(R)$ . We also show that in general $underset{ptoinfty}limunderset{mtoinfty}lim u_{m,p} eunderset{mtoinfty}limunderset{ptoinfty}lim u_{m,p}$.
Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation begin{eqnarray*} u_t+u_{xxx}+epsilon |partial_x|^{2alpha}u+(u^2)_x=0, u(0)=phi, end{eqnarray*} where $0<epsilon,alphaleq 1$ and $u$ is a real-valued function, we show that it
We study the problem of global exponential stabilization of original Burgers equations and the Burgers equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions of the controlled equations
Analytic solutions for Burgers equations with source terms, possibly stiff, represent an important element to assess numerical schemes. Here we present a procedure, based on the characteristic technique to obtain analytic solutions for these equations with smooth initial conditions.
In this paper we study global well-posedness and long time asymptotic behavior of solutions to the nonlinear heat equation with absorption, $ u_t - Delta u + |u|^alpha u =0$, where $u=u(t,x)in {mathbb R}, $ $(t,x)in (0,infty)times{mathbb R}^N$ and $a
The singular limit of the thin film Muskat problem is performed when the density (and possibly the viscosity) of the lighter fluid vanishes and the porous medium equation is identified as the limit problem. In particular, the height of the denser flu