Cauchy problems of semilinear pseudo-parabolic equations.
 作者： Yang Cao,  Jingxue Yin,  Chunpeng Wang 刊名： J. Differ. Equations, 2009, Vol.246 (12), pp.4568-4590 来源数据库： ZBMATH期刊 关键词： Sobolev type equation;  global solution;  mild solution; 原始语种摘要： The Cauchy problems $u(x,0)=u_0 (x)$, $x\in \Bbb R^n$, for semilinear Sobolev type equation $(u-\kappa \Delta u)_t = \Delta u +u^p$ in $\Bbb R^n\times\Bbb R_+$ is under consideration. Here parameters $k$, $p\in\Bbb R_+$ and function $u_0 (x)$ is nonnegative and appropriately smooth. Authors prove existence and uniquess of mild solution to this problems.? ? Main results of this paper are the following: (i) there exist global solution for each initial data in the case $0 < p \leq 1$, while there exists at least one initial data such that the solution blows up in a finite time in the case $p>1$; (ii) any nontrivial solution blows up in a finite time in the case $11+2/n$.

• 非平凡　三角洲
• solution　溶液
• equation　方程
• initial　开首字母
• semilinear　半线性的
• blows　喘息
• there　那里
• Delta　三角洲
• nontrivial　三角洲
• least　最少的