Cauchy problems of semilinear pseudo-parabolic equations.
作者: Yang CaoJingxue YinChunpeng 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 equationglobal solutionmild 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 $1

1+2/n$.

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影响因子:1.48 (2012)

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关键词翻译
关键词翻译
  • 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