Existence and uniqueness of entropy solution for nonlinear periodic parabolic problem with Orlicz growth and L^1 data

Key Points

• This paper aims to prove the existence and uniqueness of entropy solutions for a specific nonlinear periodic parabolic problem.
• Analyzed the nonlinear periodic parabolic problem using Orlicz spaces.
• Developed mathematical models represented by the equation ∂u/∂t+A(u) = f(x,t).
• Investigated properties of the Leray-Lions operator and its implications for the solutions.
• Established that an entropy solution exists for the proposed nonlinear problem.
• Demonstrated that this solution is unique under the specified Orlicz growth conditions.