Initial-Boundary Value Problem for the Camassa–Holm Equation with Linearizable Boundary Condition

2010 ◽  
Vol 96 (1-3) ◽  
pp. 123-141 ◽  
Author(s):  
Anne Boutet de Monvel ◽  
Dmitry Shepelsky
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Holm Equation ◽  
Initial Boundary Value

An initial boundary value problem of Camassa–Holm equation

2000 ◽  
Vol 41 (12) ◽  
pp. 8279-8285 ◽  
Author(s):  
Keng-Huat Kwek ◽  
Hongjun Gao ◽  
Weinian Zhang ◽  
Chaochun Qu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Holm Equation ◽  
Initial Boundary Value

Initial boundary value problem for 2D Boussinesq equations with temperature-dependent diffusion

2015 ◽  
Vol 12 (03) ◽  
pp. 469-488 ◽  
Author(s):  
Huapeng Li ◽  
Ronghua Pan ◽  
Weizhe Zhang
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Boussinesq Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Slip Boundary Condition ◽  
Heat Diffusion ◽  
2D Boussinesq Equations ◽  
Initial Boundary Value

We consider the initial-boundary value problem (IBVP) of 2D inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary. Under slip boundary condition of velocity and the homogeneous Dirichlet boundary condition for temperature, we show that there exists a unique global smooth solution to the IBVP for H3initial data. Moreover, we show that the temperature converges exponentially to zero as time goes to infinity, and the velocity and vorticity are uniformly bounded in time.

scholarly journals Initial Boundary Value Problem and Asymptotic Stabilization of the Two-Component Camassa-Holm Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Xiju Zong ◽  
Xingong Cheng ◽  
Zhonghua Wang ◽  
Zhenlai Han
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Asymptotic Stabilization ◽  
Global Asymptotic Stabilization ◽  
Holm Equation ◽  
Two Component ◽  
Initial Boundary Value

The nonhomogeneous initial boundary value problem for the two-component Camassa-Holm equation, which describes a generalized formulation for the shallow water wave equation, on an interval is investigated. A local in time existence theorem and a uniqueness result are achieved. Next by using the fixed-point technique, a result on the global asymptotic stabilization problem by means of a boundary feedback law is considered.

scholarly journals CLASSICAL SOLUTION FOR INITIAL–BOUNDARY VALUE PROBLEM FOR WAVE EQUATION WITH INTEGRAL BOUNDARY CONDITION

2012 ◽  
Vol 17 (3) ◽  
pp. 309-329 ◽  
Author(s):  
Victor Korzyuk ◽  
Victor Erofeenko ◽  
Julia Sheika
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Boundary Value Problem ◽  
Classical Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Integral Boundary Condition ◽  
Integral Boundary ◽  
Initial Boundary Value

The unique existence of classical solution of initial–boundary value problem for wave equation with a special integral boundary condition is proved in the work. Classical solution of the problem in analytical form is also found in the article. This problem arises at the modeling of electromagnetic fields with arbitrary time dependence when interaction between the field and solids is simulated with impedance boundary conditions.

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