## Solution of multilayer diffusion problems via the Laplace transform.(English)Zbl 1358.35052

In the paper, a multilayer diffusion problem is studied using the Laplace transform . Nonhomogeneous outer boundary conditions (BCs) with arbitrary time-varying functions is considered. The paper is organized as follows: Section 1 is an introduction. In Section 2 the mathematical formulation of a multilayer diffusion problem and then its reformulation as a sequence of one-layer diffusion problems with BCs that include arbitrary time-dependent functions are given. A general one-layer problem with time-varying BCs is solved in Section 3. In Section 4 the particular case of the two-layer problem is considered and an illustrative example is given. In Section 5 the authors return to the multilayer diffusion problem in order to use the results of Sections 3 and 4 for finding the solution. Finally, a discussion on the determination of critical times and brief concluding remarks are given in Section 6.

### MSC:

 35K20 Initial-boundary value problems for second-order parabolic equations

### Keywords:

multilayer; diffusion; Laplace transform; renewal equation
Full Text:

### References:

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