Existence and decay of solutions for Timoshenko-type equation with variable exponents and the supercritical damping

Key Points

• The finding demonstrates the existence of solutions for the Timoshenko-type equation under variable exponents, revealing intricate behavior related to damping.
• Key evidence presents that solutions exhibit decay under conditions of supercritical damping, highlighting the significance of this relationship.
• Method analysis focuses on Timoshenko-type equations, utilizing variable exponents to understand the behavior of solutions under varying conditions.
• This study highlights the importance of understanding the mathematical properties of these equations, suggesting further exploration in related contexts.