Classical solution of the Cauchy problem for biwave equation: Application of Fourier transform

TL;DR

This paper employs Fourier analysis techniques to derive an exact solution for the Cauchy problem associated with the n-dimensional biwave equation in the upper half-space, providing a mathematical framework for understanding this PDE.

Contribution

It introduces a Fourier transform-based method to explicitly solve the biwave equation's Cauchy problem in multiple dimensions, advancing analytical solution techniques.

Findings

Exact solution derived using Fourier analysis

Method applicable to n-dimensional biwave equations

Provides a foundation for further analytical and numerical studies

Abstract

In this paper, we use some Fourier analysis techniques to find an exact solution to the Cauchy problem for the $n$-dimensional biwave equation in the upper half-space $\mathbb{R}^n\times [0,+\infty)$.