论文标题
Banach空间中抽象的准线性演化方程的独特延续结果
Unique continuation results for abstract quasi-linear evolution equations in Banach spaces
论文作者
论文摘要
从两个不同的观点考虑了在Banach空间上定义的一类进化方程的独特延续属性：第一个观点是基于保守数量的存在，这些量经常转化为在合适的Banach空间中对系统解决方案的某些规范的保护。第二个问题是解决方案良好的问题。然后，我们的结果将应用于某些方程式，其中大多数描述了诸如波浪传播，流体动力学和可集成系统（例如$ b-$）等物理过程； Fornberg-Whitham;潜力和$π-$ CAMASSA-HOLM；广义BousSinesQ方程；和修改后的Euler-Poisson系统。
Unique continuation properties for a class of evolution equations defined on Banach spaces are considered from two different point of views: the first one is based on the existence of conserved quantities, which very often translates into the conservation of some norm of the solutions of the system in a suitable Banach space. The second one is regarded to well-posed problems. Our results are then applied to some equations, most of them describing physical processes like wave propagation, hydrodynamics, and integrable systems, such as the $b-$; Fornberg-Whitham; potential and $π-$Camassa-Holm; generalised Boussinesq equations; and the modified Euler-Poisson system.
