含对流的渗流方程的自相似解

Self-Similar Solutions to A Porous Medium Equation with Convection

摘要: 考虑含对流项的渗流方程〖SX(〗u〖〗t〖SX)〗=um+x〖WTBX〗〖DK〗SymbolQCpuq的径向自相似解的存在性，其中，qm1, x〖WTBX〗〖XC152HSW1.TIF;%85%85,JZ〗〖KG1mm〗〖KX(〗R〖KX)〗〖KG-0.8mm〗N．注意到该方程具有伸缩不变性，故可考虑形如u(x,t)=t－(t－|x|)的相似解问题．对该方程建立了相似解的存在性理论，首先确立一个临界指标q*〖KG-0.5mm〗=m+2/N, 当对流项的指标qq*时，对任意初值A0，都存在一个单调递减的整体解．而对于m

Abstract: 〖JP3〗The radial self-similar solutions of the following porous medium equation with convection 〖SX(〗u〖〗t〖SX)〗=um+x〖WTBX〗〖DK〗SymbolQCpuq 〖JP〗where qm1,x〖WTBX〗〖XC152HSW1.TIF;%85%85,JZ〗〖KG1mm〗〖KX(〗R〖KX)〗〖KG-0.8mm〗N are discussed. By the invariance properties of differential equation, this form of self-similar solutions u(x,t)=t－(t－|x|) can be considered. The existence of radial self-similar solutions is studied and a critical exponent q*〖KG-0.8mm〗=m+2/N is established. That is ,if qq*, there exists a global decreasing solution for any initial datum A0, while if m