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The entropy solution of a hyperbolic-parabolic mixed type equation
1School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024 China.
Springerplus
|November 5, 2016
Summary
This study examines entropy solutions for a specific partial differential equation, establishing solution stability under partial boundary conditions using Kruzkov
Area of Science:
- Partial Differential Equations
- Mathematical Analysis
- Numerical Analysis
Background:
- Entropy solutions are crucial for understanding conservation laws.
- Partial differential equations (PDEs) model complex physical phenomena.
- Boundary conditions significantly influence PDE solution behavior.
Purpose of the Study:
- To analyze the entropy solution of a given PDE.
- To investigate the impact of partial boundary value conditions.
- To establish the stability of these solutions.
Main Methods:
- Utilized Kruzkov's bi-variables method.
- Employed specialized test functions for analysis.
- Focused on specific domain geometries: n-dimensional cube and half-space.
Main Results:
- Demonstrated the stability of entropy solutions.
- Stability is achieved under partial boundary value imposition.
- The findings are valid for unit n-dimensional cube and half-space domains.
Conclusions:
- Kruzkov's method effectively proves solution stability for the considered PDE.
- Partial boundary conditions are sufficient for stability in specific domains.
- This research contributes to the theoretical understanding of PDEs with non-classical boundary data.
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