# Equations of Parabolic Type

Chapter

## Abstract

In this chapter we shall consider second-order parabolic equations and prove the unique solvability of the initial-boundary value problem in the domains *Q* _{ T } *=*, *(x*, *t*): *x* ∈ Ω,*t* ∈ (0, *T*) for the first, second, and third boundary conditions. We shall assume that the domain Ω is bounded, although all the results, except for the representation of solutions by Fourier series, will be valid for an arbitrary unbounded domain Ω. Moreover, the methods of solution given for bounded Ω are applicable to unbounded Ω (in particular, for Ω = *R* ^{ n }),but need minor modification which we shall point out.

## Keywords

Generalize Solution Parabolic Equation Uniqueness Theorem Unbounded Domain Integral Identity
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## Copyright information

© Springer Science+Business Media New York 1985