Existence and blow-up phenomena for a diffusion equation with variable exponent and logarithmic nonlinearity

Key Points

• The blow-up phenomenon is observed in diffusion equations with a variable exponent and logarithmic nonlinearity.
• Key evidence shows existence results and blow-up behavior, indicating critical behavior around certain solutions.
• Assessment of the diffusion equation reveals complex dynamics influenced by variable exponent and nonlinearity.
• These findings highlight the importance of understanding blow-up properties in mathematical models of diffusion.