An integral condition for the local homeomorphism property of mappings with weak derivatives

1999 ◽  
Vol 40 (6) ◽  
pp. 1134-1141 ◽  
Author(s):  
V. I. Semënov
Keyword(s):  
Integral Condition ◽  
Local Homeomorphism ◽  
Weak Derivatives

scholarly journals Hyperbolic Equations with Unknown Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1539
Author(s):  
Aleksandr I. Kozhanov
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Integral Condition ◽  
Uniqueness Theorems ◽  
Regular Solutions ◽  
Final Data ◽  
Order Hyperbolic Equation ◽  
Weak Derivatives ◽  
Second Order Hyperbolic Equation

We study the solvability of nonlinear inverse problems of determining the low order coefficients in the second order hyperbolic equation. The overdetermination condition is specified as an integral condition with final data. Existence and uniqueness theorems for regular solutions are proved (i.e., for solutions having all weak derivatives in the sense of Sobolev, occuring in the equation).

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

scholarly journals On a time fractional diffusion with nonlocal in time conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nguyen Hoang Tuan ◽  
Nguyen Anh Triet ◽  
Nguyen Hoang Luc ◽  
Nguyen Duc Phuong
Keyword(s):  
Fourier Series ◽  
Diffusion Equation ◽  
Convergence Rate ◽  
Exact Solutions ◽  
Mild Solution ◽  
Integral Condition ◽  
Fractional Diffusion ◽  
Well Posedness ◽  
Nonlocal Integral Condition ◽  
Regularized Solution

AbstractIn this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results. Firstly, we show the well-posedness and regularity for our problem. Secondly, we show the ill-posedness of our problem in the sense of Hadamard. Using the Fourier truncation method, we construct a regularized solution and present the convergence rate between the regularized and exact solutions.

scholarly journals On the maintenance of spiral structure

1979 ◽  
Vol 84 ◽  
pp. 151-153
Author(s):  
James W-K. Mark ◽  
Linda Sugiyama ◽  
Robert H. Berman ◽  
Giuseppe Bertin
Keyword(s):  
Spiral Structure ◽  
Travelling Waves ◽  
Integral Condition ◽  
Stimulated Emission ◽  
Stellar Disk ◽  
Wave System ◽  
Wave Amplification ◽  
Corotation Radius ◽  
The Galaxy ◽  
Central Regions

A concentrated nuclear bulge with about 30% of the galaxy mass is sufficient (Lin, 1975; Berman and Mark, 1978) to eliminate strong bar-forming instabilities which dominate the dynamics of the stellar disk. Weak bar-like or oval distortions might remain depending on the model. In such systems self-excited discrete modes give rise to global spiral patterns which are maintained in the presence of differential rotation and dissipation (cf. especially the spiral patterns in Bertin et al., 1977, 1978). These spiral modes are standing waves that are physically analyzable (Mark, 1977) into a superposition of two travelling waves propagating in opposite directions back and forth between galactic central regions and corotation (a resonator). Only a few discrete pattern frequencies are allowed. An interpretation is that the central regions and corotation radius must be sufficiently far apart so that a Bohr-Sommerfeld type of phase-integral condition is satisfied for the wave system of each mode. The temporal growth of these modes is mostly due to an effect of Wave Amplification by Stimulated Emission (of Rotating Spirals, abbrev. WASERS, cf. Mark 1976) which occurs in the vicinity of corotation. In some galaxies one mode might be predominent while other galaxies could exhibit more complicated spiral structure because several modes are present. Weak barlike or oval distortions hardly interfere with the structure of these modes. But they might nevertheless contribute partially towards strengthening the growth of one mode relative to another, as well as affecting the kinematics of the gaseous component.

scholarly journals Finite Difference Method for Hyperbolic Equations with the Nonlocal Integral Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Necmettin Aggez
Keyword(s):  
Space Variable ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Variable Coefficients ◽  
Difference Schemes ◽  
Order Difference ◽  
One Dimensional ◽  
Nonlocal Integral Condition ◽  
Multidimensional Hyperbolic Equations

The stable difference schemes for the approximate solution of the nonlocal boundary value problem for multidimensional hyperbolic equations with dependent in space variable coefficients are presented. Stability of these difference schemes and of the first- and second-order difference derivatives is obtained. The theoretical statements for the solution of these difference schemes for one-dimensional hyperbolic equations are supported by numerical examples.

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