论文标题
阻尼波方程的分布溶液
Distributional Solutions of the Damped Wave Equation
论文作者
论文摘要
这项工作介绍了一维阻尼波方程的解决方案，当初始条件是一般分布时，不仅是功能，也称为电报方程。对于正面和消极的时间，我们完全推论其基本解决方案。为了获得它们，我们仅使用自相似性参数和分布演算，不使用傅立叶或拉普拉斯变换。接下来，我们使用这些基本解决方案来证明分布初始值问题的解决方案的存在和独特性。作为应用程序，我们恢复了经典功能空间中初始数据的Semigroup属性，以及某种价格进化的财务模型的概率分布功能。
This work presents results on solutions of the one-dimensional damped wave equation, also called telegrapher's equation, when the initial conditions are general distributions, not only functions. We make a complete deduction of its fundamental solutions, both for positive and negative times. To obtain them we use only self-similarity arguments and distributional calculus, making no use of Fourier or Laplace transforms. We next use these fundamental solutions to prove both the existence and the uniqueness of solutions to the distributional initial value problem. As applications we recover the semigroup property for initial data in classical function spaces and also the probability distribution function for a certain financial model of evolution of prices.
