An initial boundary value problem for one-dimensional shallow water magnetohydrodynamics in the solar tachocline

2013 ◽  
Vol 76 ◽  
pp. 215-228 ◽  
Author(s):  
Ming-Cheng Shiue
Keyword(s):  
Boundary Value Problem ◽  
Shallow Water ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
One Dimensional ◽  
Initial Boundary Value ◽  
Shallow Water Magnetohydrodynamics

scholarly journals Formulation and analysis of a parabolic transmission problem on disjoint intervals

2012 ◽  
Vol 91 (105) ◽  
pp. 111-123 ◽  
Author(s):  
Bosko Jovanovic ◽  
Lubin Vulkov
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Input Data ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Well Posedness ◽  
One Dimensional ◽  
Initial Boundary Value

We investigate an initial-boundary-value problem for one dimensional parabolic equations in disjoint intervals. Under some natural assumptions on the input data we proved the well-posedness of the problem. Nonnegativity and energy stability of its weak solutions are also studied.

scholarly journals Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Lixin Tian ◽  
Qingwen Yuan ◽  
Lizhen Wang
Keyword(s):  
Boundary Value Problem ◽  
Shallow Water ◽  
Blow Up ◽  
Boundary Value ◽  
Water System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Shallow Water System ◽  
Initial Boundary Value

We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. First we prove a local in time existence theorem and present a weak-strong uniqueness result. Then, we establish a asymptotic stabilization of this system by a boundary feedback. Finally, we obtain a result of blow-up solution with certain initial data and boundary profiles.

scholarly journals Construction of a solution of a certain evolution equation II

1978 ◽  
Vol 71 ◽  
pp. 181-198 ◽  
Author(s):  
Akinobu Shimizu
Keyword(s):  
Brownian Motion ◽  
Evolution Equation ◽  
Boundary Value Problem ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
One Dimensional ◽  
Initial Boundary Value

Let D be a bounded domain in Rd with smooth boundary ∂D. We denote by Bt, t ≥ 0, a one-dimensional Brownian motion. We shall consider the initial-boundary value problem

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