共查询到20条相似文献,搜索用时 515 毫秒
1.
We study the large time behavior of the solutions of the Cauchy problem for a semilinear heat equation,
$\partial_t u=\Delta u+F(x,t,u) \quad{\rm in}
\;{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad{\rm in}
\;{\bf R}^N,\quad\quad ({\rm P})$\partial_t u=\Delta u+F(x,t,u) \quad{\rm in}
\;{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad{\rm in}
\;{\bf R}^N,\quad\quad ({\rm P}) 相似文献
2.
Fernando Bernal-Vílchis Nakao Hayashi Pavel I. Naumkin 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(3):329-355
We study the global in time existence of small classical solutions to the nonlinear Schrödinger equation with quadratic interactions of derivative type in two space dimensions $\left\{\begin{array}{l@{\quad}l}i \partial _{t} u+\frac{1}{2}\Delta u=\mathcal{N}\left( \nabla u,\nabla u\right),&;t >0 ,\;x\in {\bf R}^{2},\\ u\left( 0,x\right) =u_{0} \left( x\right),&;x\in {\bf R}^{2}, \end{array}\right.\quad\quad\quad\quad\quad\quad (0.1)$ where the quadratic nonlinearity has the form ${\mathcal{N}( \nabla u,\nabla v) =\sum_{k,l=1,2}\lambda _{kl} (\partial _{k}u) ( \partial _{l}v) }
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