scholarly journals The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity

1969 ◽  
Vol 6 (1) ◽  
pp. 71-86 ◽  
Author(s):  
Constantine M Dafermos
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
One Dimensional ◽  
Initial Boundary Value

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 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

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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