Cauchy Problem for the Biharmonic Equation in an Unbounded Domain

Abstract

The article studies the continuation of the solution to the Cauchy problem for the biharmonic equation in the domain $$G$$ from its known values on the smooth part $$S$$ of the boundary $$\partial G$$ . The considered problem belongs to the problems of mathematical physics, in which there is no continuous dependence of solutions on the initial data. It is assumed that the solution to the problem exists and is continuously differentiable in a closed domain with exactly given Cauchy data. For this case, an explicit formula for the continuation of the solution is established.

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DOI

10.3103/s1066369x25700045

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