Phase spaces for a class of Sobolev-type equations.
 作者： Georgy A. Sviridyuk 刊名： Ukr. Mat. Visn., 2004, Vol.1 (2), pp.259-272 来源数据库： ZBMATH期刊 关键词： semilinear Sobolev type equations;  relatively $p$-sectorial operator;  phase space;  Lyapunov-Schmidt method; 原始语种摘要： Summary: The solvability of the Cauchy problem $u(0)=u_0$ for a semilinear differential operator equation $L\dot u = Mu + N(u)$ is considered. Abstract results are illustrated by the Cauchy-Dirichlet problem for degenerate reaction-diffusion equations and for Navier-Stokes equations, and by the Cauchy-Bernard problem for Oskolkov thermoconvection equations.

• operator　话务员
• semilinear　半线性的
• solvability　溶解度
• sectorial　扇形的
• degenerate　退化
• relatively　比较
• problem　题目
• illustrated　以…说明
• reaction　反酌
• phase　相位