Solution of boundary value problems for the heat equation with a piecewise constant coefficient using the Fourier method
DOI:
https://doi.org/10.70474/drms4076Keywords:
Heat equation, discontinuous coefficients, eigenvalues, eigenfunctions, method of separation of variablesAbstract
This paper considers some initial boundary value problems for the heat equation in a bounded segment with a piecewise constant coefficient. Using the method of separation of variables, the problem under consideration is reduced to a spectral problem and eigenvalues and eigenfunctions of the resulting spectral problem are found. It is shown that the system of eigenfunctions forms a Riesz basis. Next, we prove a theorem on the existence and uniqueness of solutions to the initial-boundary value problems under consideration.
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