论文标题
whitham类型进化方程的解决方案的存在时间增强了
Enhanced existence time of solutions to evolution equations of Whitham type
论文作者
论文摘要
我们表明，whitham类型方程u_t + u u_x -l u_x = 0，其中l是[-1,1]，α\ neq 0的一般傅立叶乘数运算符，允许将小解决方案扩展到其预期的存在时间之外。结果对于在由α给出的分散范围内具有不均匀符号的一系列二次分散方程有效，应扩展到相同相对分散强度的其他方程。
We show that Whitham type equations u_t + u u_x -L u_x = 0, where L is a general Fourier multiplier operator of order α\in [-1,1], α\neq 0, allow for small solutions to be extended beyond their expected existence time. The result is valid for a range of quadratic dispersive equations with inhomogeneous symbols in the dispersive range given by α, and should be extendable to other equations of the same relative dispersive strength.
