Initial boundary value problem for a class of p-Laplacian equations with logarithmic nonlinearity
Fugeng Zeng1,2, Yao Huang2, Peng Shi2
1Department of Artificial Intelligence and Big Data, Yibin University, Yibin 644000, China.
Mathematical Biosciences and Engineering : MBE
|July 2, 2021
Summary
This study investigates the behavior of solutions for p-Laplacian equations with logarithmic nonlinearity, establishing conditions for global existence, boundedness, and potential blow-up or extinction of solutions.
Area of Science:
- Partial Differential Equations
- Nonlinear Analysis
- Mathematical Physics
Background:
- The study addresses the complex behavior of solutions in nonlinear partial differential equations.
- Logarithmic nonlinearities introduce unique challenges in analyzing solution dynamics.
Purpose of the Study:
- To analyze the global existence, boundedness, blow-up, and extinction properties of solutions.
- To investigate the Dirichlet boundary value problem for a specific p-Laplacian equation with logarithmic nonlinearity.
Main Methods:
- Utilizing Galerkin approximations to establish global existence of solutions.
- Applying potential well theory and the Nehari manifold to prove boundedness and blow-up.
- Deriving decay estimates and conditions for solution extinction.
Main Results:
- Global existence of solutions is established under specific conditions.
- Weak solutions are proven to be globally bounded.
- Conditions for blow-up at positive infinity are identified.
- Decay estimates and extinction properties of solutions are obtained.
Conclusions:
- The research provides a comprehensive understanding of solution behavior for the studied p-Laplacian equation.
- The findings contribute to the analysis of nonlinear evolution equations with complex nonlinear terms.
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