Proceedings of International Conference on Applied Innovation in IT  ·  2026/06/12  ·  Vol. 14  ·  Issue 4  ·  pp. 275–286
Existence and Uniqueness of Solutions for a New Model of a Triple Nonlinear Elliptic System with Various Boundary Conditions
Ahmed Abdulrahman Muhsen and Jamil Amir Ali Al-Hawasy
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Abstract
As is known, the investigation for finding the numerical solution for any mathematical model need at first to check the existence of unique analytic solution for this model. For this reason, the study for existence of a unique solution (the solvability) for any mathematical model is considered important. This importance encouraged us to devote about the study for the solvability of a new mathematical model describes by a system of triple nonlinear elliptic PDEs (TNLEPDEs) with various kinds of boundary conditions (BCs), as the Dirichlet (DBCs), the Neumann(NBCs), the Robin(RBCs) and the Mixed BCs(MBCs). In this study, the weak form (WF) for the TNLEPDEs associated with each type of the above mentioned BCs is formulated in infinite dimensional space. Then the existence theorem of a unique solution for each type of the resulted weak form is proved by utilizing the Minty-Browder theorem (MBTH), with the help of the Friedrichs- Poincare inequality (FPI) when the BCs are of homogeneous kind (HBCs) and with the help of the generalization Friedrichs- Poincare inequality (GFPI) besides to the trace operator (TRO) when the kinds of the BCs are nonhomogeneous (NHBCs).
Keywords
Drichlet Conditions Mixed Boundary Conditions Minty-Browder Theorem Numann Conditions Robin Condition Triple Nonlinear Elliptic Partial Differential Equations
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