@article{Cui2025, 
author = {Yanyan Cui and Chaojun Wang},
title = {Several boundary value problems for bi-analytic complex partial differential systems of second order},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {17117-17143},
keywords = {complex partial differential equations, Dirichlet problems, Riemann problems, bi-analytic functions, Cauchy-Pompeiu formula},
url = {https://www.sciopen.com/article/10.3934/math.2025767},
doi = {10.3934/math.2025767},
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    (  λ  ,  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    (  λ  ,  1  ) bi-analytic functions were explored on the generalized bicylinder in              C        2  . Applying the Plemelj formula, the solutions to the corresponding problems were obtained.}
}