Non-existence of Global Solutions for the Grushin Heat Equation with Nonlocal and Local Nonlinearities

Key Points

• The Grushin heat equation lacks global solutions when incorporating both local and nonlocal nonlinearities.
• Key evidence shows that these nonlinearities lead to unbounded solution behavior over time.
• Mathematical analysis of the equation reveals its inherent complexities and the challenges of solution existence.
• This finding highlights the need for alternative approaches in tackling nonlinear equations in mathematical physics.