论文标题
卷积波方程和应用的规律性属性和爆炸
The regularity properties and blow-up for convolution wave equations and applications
论文作者
论文摘要
在本文中，研究了线性和非线性卷积波方程的凯奇问题。方程涉及卷积项，具有通用核函数的卷积项，其傅立叶变换是在Banach空间E中定义的运算符函数以及某些生长条件。在这里，假设在初始数据和操作员功能上具有足够的平滑度，则根据给定部门操作员功能子的分数功率建立了解决方案的局部，全局唯一性和规律性。此外，还提供了有限的时间爆破的条件。通过选择空间E和运算符，可以获得物理领域中广泛的非局部波方程的规律性。
In this paper, the Cauchy problem for linear and nonlinear convolution wave equations are studied.The equation involves convolution terms with a general kernel functions whose Fourier transform are operator functions defined in a Banach space E together with some growth conditions. Here, assuming enough smoothness on the initial data and the operator functions, the local, global existence, uniqueness and regularity properties of solutions are established in terms of fractional powers of given sectorial operator functon. Furthermore, conditions for finite time blow-up are provided. By choosing the space E and the operators, the regularity properties the wide class of nonlocal wave equations in the field of physics are obtained.
