scholarly journals Von Neumann’s comments about existence and uniqueness for the initial-boundary value problem in gas dynamics

2009 ◽  
Vol 47 (1) ◽  
pp. 139-144 ◽  
Author(s):  
Denis Serre
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Gas Dynamics ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value

scholarly journals On Initial-Boundary Value Problem on Semiaxis for Generalized Kawahara Equation

2019 ◽  
Vol 65 (4) ◽  
pp. 683-699
Author(s):  
A. V. Faminskii ◽  
E. V. Martynov
Keyword(s):  
Boundary Value Problem ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Large Time ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Kawahara Equation ◽  
Initial Boundary Value

In this paper, we consider initial-boundary value problem on semiaxis for generalized Kawahara equation with higher-order nonlinearity. We obtain the result on existence and uniqueness of the global solution. Also, if the equation contains the absorbing term vanishing at infinity, we prove that the solution decays at large time values.

scholarly journals On dynamics of viscoelastic multidimensional medium with variable boundary

2002 ◽  
Vol 7 (9) ◽  
pp. 475-495
Author(s):  
V. P. Orlov
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Continuous Medium ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Theorems ◽  
System Of Equations ◽  
Variable Boundary ◽  
Initial Boundary Value

We prove the existence and uniqueness theorems for solutions of an initial-boundary value problem to the system of equations, which describes dynamics of viscoelastic continuous medium with a variable boundary and a memory along the trajectories of particles in classes of summable functions.

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