Fundamental solution for the Helmholtz equation in the plane

Authors

  • Davron Aslonqulovich Juraev

Keywords:

Integral formula, Matrix factorization, Helmholtz equation, Bounded domain, Cauchy problem

Abstract

This paper deals with the construction of a family of fundamental solutions of the Helmholtz equation, parameterized by an entire function with certain properties. The lemma for the Helmholtz equation on a two-dimensional bounded domain is proved.

References

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Tarkhanov, N. N. (1995). The Cauchy problem for solutions of elliptic equations. V. 7, Akad. Verl., Berlin.

Juraev, D. A. (2014). The construction of the fundamental solution of the Helmholtz equation. Reports of the Academy of Sciences of the Republic of Uzbekistan, (4), 14-17.

Juraev, D. A., & Noeiaghdam, S. (2021). Regularization of the ill-posed Cauchy problem for matrix factorizations of the Helmholtz equation on the plane. Axioms, 10(2), 1-14.

Juraev, D. A. (2021). Solution of the ill-posed Cauchy problem for matrix factorizations of the Helmholtz equation on the plane. Global and Stochastic Analysis, 8(3), 1-17.

Juraev, D. A., & Gasimov, Y. S. (2022). Regularization of the ill-posed Cauchy problem for matrix factorizations of the Helmholtz equation on the plane. Azerbaijan Journal of Mathematics, 12(1), 142-161.

Juraev, D. A., & Noeiaghdam, S. (2022). Modern Problems of Mathematical Physics and Their Applications. Axioms, 11(2), 1-6.

Juraev, D. A., & Noeiaghdam, S. (2022). Modern Problems of Mathematical Physics and Their Applications. Axioms, MDPI. Switzerland. 1-352.

Juraev, D. A. (2022). On the solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in a multidimensional spatial domain. Global and Stochastic Analysis, 9(2), 1-17.

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Published

2023-03-22