ABSTRACT
The prototype parabolic differential equation is the heat equation u xx − u y = 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493393/adca3d7b-dc1b-488c-907a-7abe95228779/content/eq1461.tif"/> and we will examine it first. Because, physically, the variable y represents time in the problem to be studied, we will set y=t and examine the heat equation in its more customary form () u t = u xx . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429493393/adca3d7b-dc1b-488c-907a-7abe95228779/content/eq1462.tif"/>
