On the Solution of an Integro-Differential Equation Using the Fourier Method
DOI:
https://doi.org/10.22105/kmisj.v2i3.101Keywords:
Hyperbolic equation, Integro-differential equation, Fourier method, Gronoull's inequalityAbstract
A nonhomogeneous integro-differential equation of viscoelasticity with zero boundary conditions is studied. To facilitate the analysis, auxiliary functions are introduced, which enable the equation to be rewritten in a form suitable for rigorous investigation. The problem is subsequently reduced to a second-kind Volterra integral equation, which is solved using the Fourier method. A theorem establishing the uniqueness of the solution to the posed problem is also proven.
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