scholarly journals Convergence of Galerkin solutions and continuous dependence on data in spectrally-hyperviscous models of 3D turbulent flow

2009 ◽  
Vol 247 (10) ◽  
pp. 2778-2798 ◽  
Author(s):  
Joel Avrin ◽  
Chang Xiao
Keyword(s):  
Turbulent Flow ◽  
Continuous Dependence ◽  
Continuous Dependence On Data

scholarly journals Anti-periodic traveling wave solutions to a class of higher-order Kadomtsev-Petviashvili-Burgers equations

1994 ◽  
Vol 7 (1) ◽  
pp. 1-12
Author(s):  
Sergiu Aizicovici ◽  
Yun Gao ◽  
Shih-Liang Wen
Keyword(s):  
Traveling Wave ◽  
Continuous Dependence ◽  
Traveling Wave Solutions ◽  
Higher Order ◽  
Two Dimensional ◽  
Burgers Equations ◽  
Wave Solutions ◽  
Periodic Traveling Wave ◽  
Continuous Dependence On Data

We discuss the existence, uniqueness, and continuous dependence on data, of anti-periodic traveling wave solutions to higher order two-dimensional equations of Korteweg-deVries type.

Continuous Dependence on Data for Solutions of Fractional Extended Fisher–Kolmogorov Equation

2018 ◽  
Vol 19 (7-8) ◽  
pp. 735-739
Author(s):  
Pengyu Chen ◽  
Zhen Xin ◽  
Jiahui An
Keyword(s):  
Boundary Value Problem ◽  
General Class ◽  
Continuous Dependence ◽  
Mild Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Kolmogorov Equation ◽  
Initial Boundary Value ◽  
Continuous Dependence On Data

AbstractThis paper is concerned with the continuous dependence of mild solutions on initial values and orders for a general class of initial boundary-value problem to fractional extended Fisher–Kolmogorov equation. The results obtained in this paper can be considered as a contribution to this emerging field.

scholarly journals Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Jin-soo Hwang
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Continuous Dependence ◽  
Dirichlet Boundary ◽  
Strong Solutions ◽  
Function Spaces ◽  
Well Posedness ◽  
Continuous Dependence On Data ◽  
Strongly Damped ◽  
Weak And Strong Solutions

We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions.

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