On fundamental solutions of a class of weak hyperbolic operators


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Authors

  • Vachagan Margaryan
  • Haik Ghazaryan

Keywords:

hyperbolic with weight operator (polynomial), multianisotropic Jevre space, Newton polyhedron, fundamental solution

Abstract

We consider a certain class of polyhedrons En, multi-anisotropic Jevre spaces G(En), their subspaces G0(En), consisting of all functions fG(En) with compact support, and their duals (G0(En)). We introduce the notion of a linear differential operator P(D), h-hyperbolic with respect to a vector NEn, where h is a weight function generated by the polyhedron . The existence is shown of a fundamental solution E of the operator P(D) belonging to (G0(En)) with suppEΩN, where ΩN:={xEn,(x,N)>0}. It is also shown that for any right-hand side fG(En) with the support in a cone contained in ΩN and with the vertex at the origin of En, the equation P(D)u=f has a solution belonging to G(En).

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Published

2024-05-26

How to Cite

Margaryan, V., & Ghazaryan, H. (2024). On fundamental solutions of a class of weak hyperbolic operators. Eurasian Mathematical Journal, 9(2). Retrieved from https://emj.enu.kz/index.php/main/article/view/116

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