Asymptotic Expansion of Solutions of Parabolic Equations with a Small Parameter

The heat equation with a small parameter, $\left( {1 + \varepsilon ^{ - m} \chi \left( {\frac{x}{\varepsilon }} \right)} \right)ut = u_{xx} $ , is considered, where ε ∈ (0, 1), m < 1 and χ is a finite function. A complete asymptotic expansion of the solution in powers ε is constructed.     

The Dependence of Solution Uniqueness Classes of Boundary Value Problems for General Parabolic Systems on the Geometry of an Unbounded Domain

General boundary value problems are considered for general parabolic (in the Douglas–Nirenberg–Solonnikov sense) systems. The dependence of solution uniqueness classes of these problems on the geometry of a nonbounded domain is established.     

Uniqueness of solutions of boundary value problems in unbounded domains for parabolic equations

The dependence of the uniqueness classes of the solutions of boundary value problems for second-order parabolic equations on the coefficients of the equation and on the geometry of an unbounded domain is investigated.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 123–136, 1988.