# Domain Perturbation for Linear and Nonlinear Parabolic Equations

## Author

**Daniel Daners**

## Status

Research Report 95-11

March 1995

## Abstract

We shall develop a general theory for domain perturbation for linear and
nonlinear parabolic equations with measurable coefficients subject to
Dirichlet boundary conditions. We show how solutions of linear and nonlinear
parabolic equations behave as a sequence of domains approaches an open set.
Convergence of domains is understood in a very general sense which allows that
certain parts of the domains degenerate and are deleted in the limit, or that
small sets are removed. We also consider the periodic problem and establish
existence and uniqueness results for periodic solutions for the perturbed
problem in a neighborhood of a periodic solution of the original equation.
The theory can be used for instance to construct domains where a given
periodic-parabolic equation has many periodic solutions.

## Key phrases

parabolic equations. perturbation. periodic solutions.

## AMS Subject Classification (1991)

Primary: 35B20

Secondary: 35K60, 35B10

## Content

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