The classical Melan equation modeling suspension bridges is considered. We first study the explicit expression and global properties of the analytical solution for the simplified ``less stiff''model, based on which we derive an a priori estimate for the original classical Melan equation and establish, under an explicit load condition, that it has a unique solution with nonnegative integral under downward live loads, thereby showing the uniqueness of the corresponding deflection curve in the engineering setting. We also develop an efficient iterative approximation method by taking the solution of the simplified ``less stiff''model as the first iterate, and prove its geometric convergence with explicit error estimates. The applicability and computational efficiency of the method are demonstrated through calculations for two actual bridges, which also quantify the influence of the nonlinear nonlocal term on the solution and clarify the relationship between the simplified and original models. Several engineering observations are verified and explained, and some related open problems are suggested.
The problem of moving inertial objects traversing simplified models of railway tracks has an analytical solution in the transformed domain under the assumptions of linearity and longitudinal homogeneity of the model. However, the time-domain response usually requires numerical integration, which could only be avoided i...
We prove local well-posedness for the modified Benjamin-Ono equation in $H^s(\mathbb{R})$ for $s>3/2$. This equation arises as a modified counterpart of the Benjamin-Ono equation through a Miura-type transformation, in close analogy with the classical relation between mKdV and KdV equations. One of the main obstacles i...
This article addresses the problem of slope stability from two complementary perspectives. On the one hand, it considers practical issues related to improving the efficiency of construction on subsidence soils. On the other hand, since traditional experimental and theoretical methods proved insufficient, it was necessa...
Aisulu Zhakulina, Adil Zhakulin, Semen S. Kuzmichev et al.· Geotechnics· 0 citations
Bressan and Shen (2021) jointly with Bressan and Murray (2020) proposed a simple example of a Cauchy problem on $\mathbb{R}^2$, characterized by two key parameters, intended to yield nonunique weak solutions of the incompressible Euler equations. They suggest that a limiting process applied to two specific approximatio...
In this article, we present a numerical analysis of the extended Fisher–Kolmogorov equation and use a mixed finite element method for its approximation. Our analysis begins with establishing the existence and uniqueness of the weak solution based on the Faedo–Galerkin approach. Next, for the fully discrete scheme, a...
Rohit Sharma, O. Yadav· Numerical Methods for Partia...· 0 citations
