Work

Several boundary value problems for bi-analytic complex partial differential systems of second order

Year: 2025

Type: article

Abstract: In this paper, several boundary value problems for second order complex partial differential systems of bi-analytic functions were investigated on the bicylinder. Homogeneous and nonhomogeneous Dirichlet problems for $ (\lambda, 1) $ bi-analytic functions were first discussed on the bicylinder. Applying the Cauchy-Pompeiu formula and the properties of the Poisson kernel, the expressions of the solutions to the Dirichlet problems were obtained. Thereafter, the Riemann problems and the inverse problems for $ (\lambda, 1) $ bi-analytic functions were explored on the generalized bicylinder in $ \mathbb{C}^2 $. Applying the Plemelj formula, the solutions to the corresponding problems were obtained.

Source: AIMS Mathematics

DOI: 10.3934/math.2025767

Authors: Yanyan Cui, Chaojun Wang

Institution: Zhoukou Normal University

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Science Foundation, National Natural Science Foundation of China, Education Department of Henan Province