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Initial‐to‐Interface Maps for the Heat Equation on Composite Domains
Author(s) -
Sheils Natalie E.,
Deconinck Bernard
Publication year - 2016
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12138
Subject(s) - interface (matter) , boundary value problem , heat equation , mathematical analysis , function (biology) , mathematics , initial value problem , derivative (finance) , geometry , mechanics , physics , bubble , maximum bubble pressure method , evolutionary biology , financial economics , economics , biology
A map from the initial conditions to the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with n interfaces. The existence of this map allows changing the problem at hand from an interface problem to a boundary value problem which allows for an alternative to the approach of finding a closed‐form solution to the interface problem.