scholarly journals The self-similar solutions of the one-dimensional semilinear Tricomi-type equations

2007 ◽  
Vol 236 (1) ◽  
pp. 82-115 ◽  
Author(s):  
Karen Yagdjian
Keyword(s):  
The Self ◽  
One Dimensional ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

On the stability of a class of self-similar solutions to the filtration-absorption equation

2002 ◽  
Vol 13 (2) ◽  
pp. 179-194 ◽  
Author(s):  
ALINA CHERTOCK
Keyword(s):  
The Self ◽  
Initial Condition ◽  
Cauchy Problems ◽  
One Dimensional ◽  
Self Similar ◽  
Analytical Result ◽  
Axisymmetric Solutions ◽  
The Stability ◽  
The One ◽  
Similar Solutions

We consider the one-dimensional and two-dimensional filtration-absorption equation ut = uΔu−(c−1)(∇u)2. The one-dimensional case was considered previously by Barenblatt et al. [4], where a special class of self-similar solutions was introduced. By the analogy with the 1D case we construct a family of axisymmetric solutions in 2D. We demonstrate numerically that the self-similar solutions obtained attract the solutions of non-self-similar Cauchy problems having the initial condition of compact support. The main analytical result we provide is the linear stability of the above self-similar solutions both in the 1D case and in the 2D case.

A self-similar solution for expansion into a vacuum of a collisionless plasma bunch

1998 ◽  
Vol 59 (1) ◽  
pp. 83-90 ◽  
Author(s):  
A. V. BAITIN ◽  
K. M. KUZANYAN
Keyword(s):  
Electron Distribution Function ◽  
Collisionless Plasma ◽  
Electron Component ◽  
One Dimensional ◽  
Ultrarelativistic Electron ◽  
Plasma Bunch ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

The process of expansion into a vacuum of a collisionless plasma bunch with relativistic electron temperature is investigated for the one-dimensional case. Self-similar solutions for the evolution of the electron distribution function and ion acceleration are obtained, taking account of cooling of the electron component of plasma for the cases of non-relativistic and ultrarelativistic electron energies.

Theoretical modeling of the carbon dioxide injection into the porous medium saturated with methane and water taking into account the CO2 hydrate formation

2018 ◽  
Author(s):  
Gubaidullin A. A. ◽  
Musakaev N. G. ◽  
Duong Ngoc Hai ◽  
Borodin S. L. ◽  
Nguyen Quang Thai ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Hydrate Formation ◽  
Carbon Dioxide Injection ◽  
Reservoir Temperature ◽  
One Dimensional ◽  
Porous Reservoir ◽  
Self Similar ◽  
The One ◽  
Similar Solutions ◽  
The Mathematical Model

In this work the mathematical model is constructed and the features of the injection of warm carbon dioxide (with the temperature higher than the initial reservoir temperature) into the porous reservoir initially saturated with methane gas and water are investigated. Self-similar solutions of the one-dimensional problem describing the distributions of the main parameters in the reservoir are constructed. The effect of the parameters of the injected carbon dioxide and the reservoir on the intensity of the CO2 hydrate formation is analyzed

scholarly journals Impact of dust in the decay of blast waves produced by a nuclear explosion

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200105 ◽  
Author(s):  
Meera Chadha ◽  
J. Jena
Keyword(s):  
Radiation Effects ◽  
Nuclear Explosion ◽  
Blast Waves ◽  
Dust Particles ◽  
One Dimensional ◽  
Self Similar ◽  
The One ◽  
Similar Solutions ◽  
The Impact ◽  
Relaxing Gas

In this paper, we have studied the impact created by the introduction of up to 5% dust particles in enhancing the decay of blast waves produced by a nuclear explosion. A mathematical model is designed and modified using appropriate assumptions, the most important being treating a nuclear explosion as a point source of energy. A system of partial differential equations describing the one-dimensional, adiabatic, unsteady flow of a relaxing gas with dust particles and radiation effects is considered. The symmetric nature of an explosion is captured using the Lie group invariance and self-similar solutions obtained for the gas undergoing strong shocks. The enhancements in decay caused by varying the quantity of dust are studied. The energy released and the damage radius are found to decrease with time with an increase in the dust parameters.

Comments on the paper ‘Self-similar state of a weakly turbulent plasma’

1982 ◽  
Vol 27 (1) ◽  
pp. 189-190 ◽  
Author(s):  
G. E. Vekstein ◽  
D. D. Ryutov ◽  
R. Z. Sagdeev
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Collisionless Plasma ◽  
Turbulent Plasma ◽  
The Self ◽  
Similar Solution ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One

In a recent paper, Balescu (1980) criticizes the self-similar solution in the problem of anomalous plasma resistivity (Vekstein, Ryutov & Sagdeev 1970) and comes to the conclusion that this solution is not correct. The aim of this comment is to show why Balescu's arguments are erroneous.We consider here the simplest case of the one-dimensional collisionless plasma in the presence of an external electric field.

scholarly journals Self-similar solutions of the one-dimensional Landau–Lifshitz–Gilbert equation

Nonlinearity ◽  
2015 ◽  
Vol 28 (5) ◽  
pp. 1307-1350 ◽  
Author(s):  
Susana Gutiérrez ◽  
André de Laire
Keyword(s):  
One Dimensional ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

Self-similar solutions for Vlasov and water-bag models

1978 ◽  
Vol 19 (1) ◽  
pp. 135-146 ◽  
Author(s):  
J. R. Burgan ◽  
J. Gutierrez ◽  
E. Fijalkow ◽  
M. Navet ◽  
M. R. Feix
Keyword(s):  
Single Species ◽  
Complete Agreement ◽  
Self Similarity ◽  
One Dimensional ◽  
Virtual Particle ◽  
Electron Plasmas ◽  
Finite Group Theory ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

Using finite group theory, self-similar solutions for the one-dimensional Vlasov– Poisson system are considered, both for electron plasmas, with a fixed ion background, and for a single species beam. Difficulties arising from the Poisson equation are pointed out and handled by using an exponential group of transformations. Introducing, for the beam, a water-bag model, we find that the boundary condition problem, imposed by self-similarity, can be solved through the introduction of a ‘virtual particle’ concept. In order to test the analytical solution obtained, we perform a numerical simulation using a particle code. Complete agreement is found.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

Spin-Wave Spectrum in the Sinusoidal Superlattice with Amplitude and Phase Inhomogeneities

2014 ◽  
Vol 215 ◽  
pp. 385-388
Author(s):  
Valter A. Ignatchenko ◽  
Denis S. Tsikalov
Keyword(s):  
Spin Wave ◽  
Density Of States ◽  
Wave Spectrum ◽  
The Self ◽  
One Dimensional ◽  
Consistent Approximation ◽  
Self Consistent ◽  
Greens Function ◽  
The One ◽  
Spin Wave Spectrum

Effects of both the phase and the amplitude inhomogeneities of different dimensionalities on the Greens function and on the one-dimensional density of states of spin waves in the sinusoidal superlattice have been studied. Processes of multiple scattering of waves from inhomogeneities have been taken into account in the self-consistent approximation.

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