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 problem;  semilinear Sobolev-type equation;  plane-parallel heat convection;  viscous incompressible Kelvin-Voight fluid;  quasistationary 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.

• 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