The space of initial data of the 3d boundary-value problem for a parabolic differential-difference equation in the one-dimensional case

2012 ◽  
Vol 92 (3-4) ◽  
pp. 580-584 ◽  
Author(s):  
A. M. Selitskii
Keyword(s):  
Initial Data ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Dimensional Case ◽  
One Dimensional ◽  
Differential Difference Equation ◽  
The One

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

scholarly journals Spectral analysis of Hahn-Dirac system

2021 ◽  
Author(s):  
Bilender Allahverdiev ◽  
Hüseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Boundary Value Problem ◽  
Spectral Properties ◽  
Orthonormal Basis ◽  
Boundary Value ◽  
Dirac System ◽  
One Dimensional ◽  
Countable Sequence ◽  
Greens Function ◽  
The One

In this paper, we study some spectral properties of the one-dimensional Hahn-Dirac boundary-value problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Greens function, the existence of a countable sequence of eigenvalues, eigenfunctions forming an orthonormal basis of L2w,q ((w0. a): E).

FROM BOUNDARY VALUE PROBLEMS TO DIFFERENCE EQUATIONS: A METHOD OF INVESTIGATION OF CHAOTIC VIBRATIONS

1999 ◽  
Vol 09 (07) ◽  
pp. 1285-1306 ◽  
Author(s):  
E. YU. ROMANENKO ◽  
A. N. SHARKOVSKY
Keyword(s):  
Difference Equation ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Boundary Value ◽  
Dynamical Behavior ◽  
Time Behavior ◽  
One Dimensional ◽  
Long Time ◽  
The Difference ◽  
The One

Among evolutionary boundary value problems for partial differential equations, there is a wide class of problems reducible to difference, differential-difference and other relevant equations. Of especial promise for investigation are problems that reduce to difference equations with continuous argument. Such problems, even in their simplest form, may exhibit solutions with extremely complicated long-time behavior to the extent of possessing evolutions that are indistinguishable from random ones when time is large. It is owing to the reduction to a difference equation followed by the employment of the properties of the one-dimensional map associated with the difference equation, that, it is in many cases possible to establish mathematical mechanisms for one or other type of dynamical behavior of solutions. The paper presents the overall picture in the study of boundary value problems reducible to difference equations (on which the authors have a direct bearing over the last ten years) and demonstrates with several simplest examples the potentialities that such a reduction opens up.

Sign in / Sign up

Export Citation Format

Share Document