scholarly journals Solvability of an Initial-Boundary Value Problem for a Second Order Parabolic System with a Third Order Dispersion Term

2012 ◽  
Vol 44 (5) ◽  
pp. 3388-3411 ◽  
Author(s):  
Masashi Aiki ◽  
Tatsuo Iguchi
Keyword(s):  
Boundary Value Problem ◽  
Parabolic System ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Third Order ◽  
Third Order Dispersion ◽  
Initial Boundary Value ◽  
Order Dispersion ◽  
Dispersion Term

scholarly journals On a third order initial boundary value problem in a plane domain

2012 ◽  
Vol 17 (3) ◽  
pp. 312-326
Author(s):  
Neringa Klovienė
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Plane Domain ◽  
Third Order ◽  
Initial Boundary Value

Third order initial boundary value problem is studied in a bounded plane domain σ with C4 smooth boundary ∂σ. The existence and uniqueness of the solution is proved using Galerkin approximations and a priory estimates. The problem under consideration appear as an auxiliary problem by studying a second grade fluid motion in an infinite three-dimensional pipe with noncircular cross-section.

LOCAL SOLVABILITY OF AN INITIAL BOUNDARY VALUE PROBLEM FOR A QUASILINEAR HYPERBOLIC-PARABOLIC SYSTEM

2006 ◽  
Vol 03 (02) ◽  
pp. 195-232 ◽  
Author(s):  
YOSHIYUKI KAGEI ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Boundary Value Problem ◽  
Transport Equation ◽  
Parabolic System ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Local Solvability ◽  
Continuous Functions ◽  
Initial Boundary Value ◽  
Time Existence

This paper investigates the solvability of initial boundary value problem for a quasilinear hyperbolic-parabolic system which consists of a transport equation and strongly parabolic system. The characteristics of the transport equation are assumed to be outward on the boundary of the domain. The unique local (in time) existence of solutions is shown in the class of continuous functions with values in Hs, where s is an integer satisfying s ≥ [n/2]+1.

scholarly journals A numerical method for solving the second initial-boundary value problem for a multidimensional third-order pseudoparabolic equation

2021 ◽  
Vol 31 (3) ◽  
pp. 384-408
Author(s):  
M.Kh. Beshtokov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Pseudoparabolic Equation ◽  
Third Order ◽  
One Dimensional ◽  
Initial Boundary Value

The work is devoted to the study of the second initial-boundary value problem for a general-form third-order differential equation of pseudoparabolic type with variable coefficients in a multidimensional domain with an arbitrary boundary. In this paper, a multidimensional pseudoparabolic equation is reduced to an integro-differential equation with a small parameter, and a locally one-dimensional difference scheme by A.A. Samarskii is used. Using the maximum principle, an a priori estimate is obtained for the solution of a locally one-dimensional difference scheme in the uniform metric in the $C$ norm. The stability and convergence of the locally one-dimensional difference scheme are proved.

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