On the generalized heat-equation

Abstract

The general heat equation is defined aswhere v is a fixed positive number and α is a fixed number. If v = α = 0, then (1.1) reduces to the ordinary heat equationwhere u(x,t) is regarded as the temperature at a point x at time t, in an infinite insulated rod extended along the x-axis in the xt-plane. If we set , then (1.1) becomes