Self-similar Solutions for a Nonlinear Heat Equation Modelling MEMS

This paper deals with the existence and nonexistence of self-similar solutions for a nonlinear heat equation arising from electrostatic MEMS. We show that there exists a critical value A*, such that if the initial data is less than A*, then there is no global forward self-similar radial solution. While if the initial data is greater than A*, then there exists a family of increasing global forward self-similar radial solutions, which goes to ∞ as r → ∞. We also establish the optimal growth rate of these solutions. At last, we give the nonexistence result of backward self-similar solutions.