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Research Article Open access CC BY 4.0

Self-similar Solutions for a Nonlinear Heat Equation Modelling MEMS

Jian Deng

Current Journal of Applied Science and Technology · pp. 1–8 · Published 18 Jun 2016

10.9734/BJAST/2016/26468

Abstract

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.

Forward self-similar solutions backward self-similar solutions heat equation MEMS

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