Existence and uniqueness result for a class of mixed variational problems

Area of Science:

• Mathematics
• Applied Mathematics
• Numerical Analysis

Background:

• Mixed variational problems are crucial in modeling complex physical phenomena.
• Understanding their existence and uniqueness is fundamental for developing reliable numerical solutions.
• Variational inequalities form the mathematical basis for these problems.

Purpose of the Study:

• To establish the existence and uniqueness of solutions for a specific class of mixed variational problems.
• To demonstrate the applicability of saddle-point theory to these problems.
• To provide practical examples through frictional contact mechanics.

Main Methods:

• The core methodology involves the application of saddle-point theory.
• This theoretical framework is used to analyze the governing system of two variational inequalities.
• The approach ensures rigorous mathematical treatment of the problem.

Main Results:

• The paper successfully demonstrates the existence of solutions for the investigated mixed variational problems.
• Uniqueness of these solutions is also established under the given conditions.
• The theoretical results are validated through concrete examples.

Conclusions:

• The study confirms the efficacy of saddle-point theory in solving mixed variational problems.
• The findings contribute to the theoretical understanding of variational inequalities.
• The presented frictional contact problems serve as practical validations of the established results.