Parabolic equations

Abstract

In this chapter we consider parabolic equations of the form

$$\frac{\partial u}{\partial t}+Lu=f,\qquad \bf X\in\it \Omega,\;t>0$$

where $\it \Omega$ is a domain of $\mathbb{R}^d, d=1,2,3\;f=f(\bf X,t)$ is a given function, $L=L(\bf X)$ is a generic elliptic operator acting on the unknown $u=u(\bf X,t)$.