On a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions

TL;DR

This paper derives an explicit representation of the weak solution for a higher-order linear PDE in two variables with initial conditions involving real-valued step functions, using an advanced matrix method.

Contribution

It introduces a novel application of infinite-dimensional cellular matrices to explicitly solve higher-order PDEs with step function coefficients.

Findings

Explicit weak solution representation obtained

Method applicable to PDEs with step function coefficients

Enhances analytical tools for complex PDEs

Abstract

By using the method developed in the paper [G.Pantsulaia, G.Giorgadze, On some applications of infinite-dimensional cellular matrices, {\it Georg. Inter. J. Sci. Tech., Nova Science Publishers,} Volume 3, Issue 1 (2011), 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions