Solvability of the Cauchy problem of a semilinear Sobolev type equation with a relatively sectorial operator.
作者: T.A. Bokareva
刊名: Differ. Equations, 1996, Vol.32 (6), pp.819-825
来源数据库: ZBMATH期刊
关键词: Cauchy problemsemilinear Sobolev-type equationplane-parallel heat convectionviscous incompressible Kelvin-Voight fluidquasistationary semitrajectory
原始语种摘要: The paper deals with the Cauchy problem of the semilinear Sobolev-type equation $L\dot u= Mu+F(u)$, where $L$, $M$, and $F$ are, respectively, continuous linear, closed linear, and nonlinear smooth operators acting in related Banach spaces. A specific case of this equation models a plane-parallel heat convection in a layer of a viscous incompressible Kelvin-Voight fluid. Using the introduced property of operator $M$ to be sectorial with respect to the operator $L$ with number $p=0,1,\dots$, the author constructs the phase space of the above equation. This allows one to give a sufficient condition for the existence of a unique solution of the Cauchy problem which is its quasistationary semitrajectory.
全文获取路径: ZBMATH 
影响因子:0.42 (2012)

  • operator 话务员
  • semilinear 半线性的
  • incompressible 不可压缩的
  • equation 方程
  • viscous 粘滞的
  • problem 题目
  • sectorial 扇形的
  • fluid 
  • convection 对流