| Autor: |
GUTLYANSKI, VLADIMIR, NESMELOVA, OLGA, RYAZANOV, VLADIMIR, YAKUBOV, EDUARD |
| Předmět: |
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| Zdroj: |
Constructive Mathematical Analysis; Sep2023, Vol. 6 Issue 3, p151-163, 13p |
| Abstrakt: |
We study the semi-linear Beltrami equation ω¯z - µ(z)ωz = σ(z)q(ω(z)) and show that it is closely related to the corresponding semi-linear equation of the form divA(z)U(z) = G(z)Q(U(z)). Applying the theory of completely continuous operators by Ahlfors-Bers and Leray--Schauder, we prove existence of regular solutions both to the semi-linear Beltrami equation and to the given above semi-linear equation in the divergent form, see Theorems 1.1 and 5.2. We also derive their representation through solutions of the semi-linear Vekua type equations and generalized analytic functions with sources. Finally, we apply Theorem 5.2 for several model equations describing physical phenomena in anisotropic and inhomogeneous media. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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