Traveling waves with singularities in a damped hyperbolic MEMS type equation in the presence of negative powers nonlinearity
Date
2023-01-16
Authors
Ichida, Yu
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider traveling waves with singularities in a damped hyperbolic MEMS type equation in the presence of negative powers nonlinearity. We investigate how the existence of traveling waves, their shapes, and asymptotic behavior change with the presence or absence of an inertial term. These are studied by applying the framework that combines Poincare compactification, classical dynamical systems theory, and geometric methods for the desingularization of vector fields. We report that the presence of this term causes the shapes to change significantly for sufficiently large wave speeds.
Description
Keywords
MEMS type equation, Poincare compactification, Desingularization of vector fields (blow-up), Asymptotic behavior
Citation
Ichida, Y. (2023). Traveling waves with singularities in a damped hyperbolic MEMS type equation in the presence of negative powers nonlinearity. <i>Electronic Journal of Differential Equations, 2023</i>(05), pp. 1-20.
Rights
Attribution 4.0 International