scholarly journals Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation

2019 ◽  
Vol 24 (1) ◽  
pp. 197-209
Author(s):  
Aslihan Demirkaya ◽  
◽  
Milena Stanislavova ◽  
Keyword(s):  
Fourth Order ◽  
Traveling Waves ◽  
Numerical Results ◽  
Beam Equation ◽  
Existence And Stability ◽  
Standing And Traveling Waves

scholarly journals Standing And Traveling Waves On Transmission Lines:Getting It Right

2020 ◽  
Author(s):  
Raymond Jacquot ◽  
David Voltmer ◽  
John Steadman
Keyword(s):  
Traveling Waves ◽  
Standing And Traveling Waves

scholarly journals Existence and stability of fourth-order nonlinear plate problem

2019 ◽  
Vol 6 (1) ◽  
pp. 81-98
Author(s):  
Salim A. Messaoudi ◽  
Soh Edwin Mukiawa
Keyword(s):  
Weak Solution ◽  
Fourth Order ◽  
Stability Result ◽  
Suspension Bridge ◽  
Global Weak Solution ◽  
Restoring Force ◽  
Nonlinear Plate ◽  
Frictional Damping ◽  
Existence And Stability

AbstractIn this paper, we study a fourth-order plate problem as a model for a suspension bridge in the presence of a nonlinear frictional damping and a hanger restoring force. We establish the existence of a global weak solution and prove a stability result.

scholarly journals Existence of Positive Solutions of a Discrete Elastic Beam Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Ruyun Ma ◽  
Jiemei Li ◽  
Chenghua Gao
Keyword(s):  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Elastic Beam ◽  
Beam Equation ◽  
Nonlinear Boundary Value Problems ◽  
Order Difference ◽  
Bifurcation Theorem ◽  
Existence Of Positive Solutions

LetTbe an integer withT≥5and letT2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equationsΔ4u(t−2)−ra(t)f(u(t))=0,t∈T2,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, whereris a constant,a:T2→(0,∞),  and  f:[0,∞)→[0,∞)is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

scholarly journals Hyperbolic traveling waves driven by growth

2014 ◽  
Vol 24 (06) ◽  
pp. 1165-1195 ◽  
Author(s):  
Emeric Bouin ◽  
Vincent Calvez ◽  
Grégoire Nadin
Keyword(s):  
Nonlinear Stability ◽  
Traveling Waves ◽  
Hyperbolic Model ◽  
Kpp Equation ◽  
Transition Parameter ◽  
Minimal Speed ◽  
Traveling Fronts ◽  
Traveling Front ◽  
Maximal Speed ◽  
Existence And Stability

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed ϵ-1 (ϵ > 0), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter ϵ: for small ϵ the behavior is essentially the same as for the diffusive Fisher-KPP equation. However, for large ϵ the traveling front with minimal speed is discontinuous and travels at the maximal speed ϵ-1. The traveling fronts with minimal speed are linearly stable in weighted L2 spaces. We also prove local nonlinear stability of the traveling front with minimal speed when ϵ is smaller than the transition parameter.

Existence and stability of invasion traveling waves for a competition system with random vs. nonlocal dispersals

2019 ◽  
Vol 12 (01) ◽  
pp. 1950004
Author(s):  
Jiao Wang ◽  
Zhixian Yu ◽  
Yanling Meng
Keyword(s):  
Traveling Waves ◽  
Weighted Spaces ◽  
Nonlocal Dispersal ◽  
Asymptotic Behaviors ◽  
Competition System ◽  
Weighted Energy ◽  
Existence And Stability ◽  
Exponentially Stable ◽  
Exponentially Weighted

The purpose of this paper is to investigate asymptotic behaviors of the solutions for a competition system with random vs. nonlocal dispersal. We first prove the existence of invasion traveling waves via using the theory of asymptotic speeds of spread. Then we prove the invasion traveling waves are exponentially stable as perturbation in some exponentially weighted spaces by using the weighted energy and the squeezing technique.

Sign in / Sign up

Export Citation Format

Share Document