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The growth or decay estimates for nonlinear wave equations with damping and source terms
Peng Zeng1, Dandan Li1, Yuanfei Li1
1School of Data Science, Guangzhou Huashang College, Guangdong 511300, China.
Mathematical Biosciences and Engineering : MBE
|September 7, 2023
Summary
This study analyzes nonlinear wave equations, providing faster spatial decay and growth estimates for solutions in cylindrical or exterior regions. These findings improve energy bounds and extend to viscoelastic systems.
Area of Science:
- Nonlinear Partial Differential Equations
- Mathematical Physics
- Wave Phenomena
Background:
- Understanding the spatial behavior of solutions is crucial for nonlinear wave equations.
- Existing literature provides estimates for growth and decay rates, but improvements are sought.
Purpose of the Study:
- To investigate the spatial decay and growth behavior of coupled nonlinear wave equations.
- To derive improved estimates for solutions in specific geometries.
- To extend the analysis to nonlinear viscoelastic systems.
Main Methods:
- Analysis of coupled nonlinear wave equations defined in cylindrical or exterior domains.
- Application of specific boundary conditions to derive estimates.
- Extension of methods to nonlinear viscoelastic systems.
Main Results:
- Obtained spatial growth and decay estimates for solutions under specific boundary conditions.
- Demonstrated that the derived growth/decay rates are faster than those in existing literature.
- Proved that total energy can be bounded by known data in decay cases.
Conclusions:
- The study provides refined spatial behavior estimates for nonlinear wave equations.
- The findings offer significant improvements over previous results and have broader applicability.
- The energy boundedness results are valuable for stability analysis.
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