Asymptotic properties of quenching for the quasilinear electrostatic micro-electro-mechanical system

This study focuses on the asymptotic properties of quenching solutions for the quasilinear parabolic electrostatic micro-electro-mechanical system with singular logarithm boundary flux. Under some assumptions on initial data, quenching in finite time, blowup phenomenon of a time derivative, lower and upper bounds of quenching rate are studied theoretically, and the asymptotic behaviors near quenching time are verified numerically.

Nonexistence of Global Solutions for Coupled System of Pseudoparabolic Equations with Variable Exponents and Weak Memories

The most important behavior for evolution system is the blow-up phenomena because of its wide applications in modern science. The article discusses the finite time blowup that arise under an appropriate conditions. The nonsolvability of boundary value problem for damped pseudoparabolic differential equations with variable exponents is investigated. Such problem has been previously studied in the case if p and q are constants. New here is the case of variables of nonlinearity p and q which make the problem has a scientific interest.