Graduate School of Science and Technology
Meiji University, 1-1-1
Higashimita Tama-ku Kawasaki Kanagawa 214-8571, Japan
email: ichidayu@meiji.ac.jp
Yu Ichida
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.
Submitted June 22, 2022. Published January 16, 2023.
Math Subject Classifications: 34C05, 34C08, 35B40, 35C07, 35L81, 74H35.
Key Words: MEMS type equation; Poincare compactification;
Desingularization of vector fields (blow-up); Asymptotic behavior.
DOI: https://doi.org/10.58997/ejde.2023.05
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Yu Ichida Graduate School of Science and Technology Meiji University, 1-1-1 Higashimita Tama-ku Kawasaki Kanagawa 214-8571, Japan email: ichidayu@meiji.ac.jp |
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