J. Korean Math. Soc. 2017; 54(3): 945-966
Online first article April 7, 2017 Printed May 1, 2017
https://doi.org/10.4134/JKMS.j160317
Copyright © The Korean Mathematical Society.
Semion Gutman and Junhong Ha
University of Oklahoma, Korea University of Technology and Education
The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.
Keywords: shallow arch equation, strong damping, regularization of solutions
MSC numbers: 37L05, 35B40, 35Q74
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