Applications of the L_2-Transform to Partial Differential Equations

TL;DR

This paper explores the use of the L_2-integral transform in solving partial differential equations, highlighting its application to specific PDEs and introducing related properties and convolutions.

Contribution

It demonstrates the applicability of the L_2-transform to PDEs, including those of exponential squared order, and discusses its properties and convolution operations.

Findings

L_2-transform effectively solves certain PDEs

Application to PDEs of exponential squared order

Introduction of L_2 convolution method

Abstract

This paper aims to demonstrate the applicability of the L_2-integral transform to Partial Differential Equations (PDEs). Of special interest is section (6), which contains an application of the L_2-transform to a PDE of exponential squared order, but not of exponential order. Sections (1) and (2) aim to introduce the history and some elementary properties of the L_2-transform, (3) and (4) include some of the transform's simple applications, and section (5) introduces the L_2 convolution.