Exact solutions of the boundary-value problems for the Helmholtz\n equation in a layer with polynomials in the right-hand sides of the equation\n and of the boundary conditions

2020/01/23 by Oleg D. Algazin, Algazin, Oleg D.
Mathematics · Engineering · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Material Science and Thermodynamics

paper · pdf · doi:10.48550/arxiv.2001.09808

Abstract

In a multidimensional infinite layer bounded by two hyperplanes, the\ninhomogeneous Helmholtz equation with a polynomial right-hand side is\nconsidered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value\nproblems with polynomials in the right-hand sides of the boundary conditions\nhave a solution that is a quasipolynomial that contains, in addition to the\npower functions, also hyperbolic or trigonometric functions. This solution is\nunique in the class of slow growth functions if the parameter of the equation\nis not an eigenvalue. An algorithm for constructing this solution is given and\nexamples are considered.\n

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