Domain Decomposition Scheme for First-Order Evolution Equations with Nonselfadjoint Operators

2013 ◽  
pp. 279-302 ◽  
Author(s):  
Petr Vabishchevich ◽  
Petr Zakharov
Keyword(s):  
Domain Decomposition ◽  
Evolution Equations ◽  
First Order ◽  
Decomposition Scheme

scholarly journals On the stability of first order impulsive evolution equations

2014 ◽  
Vol 34 (3) ◽  
pp. 639 ◽  
Author(s):  
JinRong Wang ◽  
Michal Fečkan ◽  
Yong Zhou
Keyword(s):  
Evolution Equations ◽  
First Order ◽  
The Stability ◽  
Impulsive Evolution Equations

On Some Game Problems for First-Order Controlled Evolution Equations

2005 ◽  
Vol 41 (8) ◽  
pp. 1169-1177 ◽  
Author(s):  
N. Yu. Satimov ◽  
M. Tukhtasinov
Keyword(s):  
Evolution Equations ◽  
First Order

A METHOD TO CONSTRUCT WEIERSTRASS ELLIPTIC FUNCTION SOLUTION FOR NONLINEAR EQUATIONS

2011 ◽  
Vol 25 (14) ◽  
pp. 1931-1939 ◽  
Author(s):  
LIANG-MA SHI ◽  
LING-FENG ZHANG ◽  
HAO MENG ◽  
HONG-WEI ZHAO ◽  
SHI-PING ZHOU
Keyword(s):  
Nonlinear Equations ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Order Derivative ◽  
First Order ◽  
Function Solution ◽  
Weierstrass Elliptic Function ◽  
Klein Gordon

A method for constructing the solutions of nonlinear evolution equations by using the Weierstrass elliptic function and its first-order derivative was presented. This technique was then applied to Burgers and Klein–Gordon equations which showed its efficiency and validality for exactly some solving nonlinear evolution equations.

Game problems on a fixed interval in controlled first-order evolution equations

2006 ◽  
Vol 80 (3-4) ◽  
pp. 578-589 ◽  
Author(s):  
N. Yu. Satimov ◽  
M. Tukhtasinov
Keyword(s):  
Evolution Equations ◽  
Fixed Interval ◽  
First Order

scholarly journals Hydrodynamic Model Of Glaciers and Ice Sheets Interacted With Ocean

1990 ◽  
Vol 14 ◽  
pp. 347-347
Author(s):  
V.L. Mazo
Keyword(s):  
Shear Stress ◽  
Hydrodynamic Model ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Longitudinal Stress ◽  
First Order ◽  
Longwave Approximation ◽  
Different Parts

Tidewater glaciers and large ice sheets, e.g. the Antarctic ice sheet and a late-Würm Arctic ice sheet, are complex but single dynamic systems composed of terrestrial, marine and floating parts. Morphology and dynamics of the different parts are different. The terrestrial parts are convex and their dynamics are controlled by shear stress only (the longitudinal stress is zero); the floating parts are concave and their dynamics are controlled by longitudinal stress only (the shear stress is zero). To connect the different parts we should consider transitional zones where shear and longitudinal stresses are comparable.To describe glacier and ice-sheet dynamics, longwave approximation of the first order is used. In this approximation it is impossible to connect terrestrial and floating parts dynamically, only morphologically and kinematically. It means that the first-order longwave approximation is not sufficient.If the transitional zone between the terrestrial and floating parts is long in comparison to ice thickness (in hydrodynamics the term “weak” is used) we can do the next step in the longwave approximation to describe the single dynamical system consisting of the terrestrial and floating parts and the weak transitional zones (ice streams). It is a purely hydrodynamical approach to the problem without ad hoc hypothesis.The presented model is a non-stationary three-dimensional hydrodynamic model of glaciers and ice sheets interacted with ocean, involving the conditions of ice continuity and dynamic equilibrium, ice rheology, and boundary conditions on the free surface (dynamic and kinematic) and on the bed (ice freezing or sliding). Longwave approximation is used to reduce the three-dimensional model to a two-dimensional one. The latter consists of (1) evolution equations for grounded and floating parts and weak transitional zones; (2) boundary conditions on the fronts (e.g. the conditions of calving); (3) equations governing the junctions of the parts (the most important junction is the grounded line) with the conditions connecting the evolution equations.

On the structure of conformal singularities in classical general relativity. II Evolution equations and a conjecture of K. P. Tod

1993 ◽  
Vol 443 (1919) ◽  
pp. 493-515 ◽  
Keyword(s):  
Large Scale ◽  
Evolution Equations ◽  
Physical Space ◽  
Space Time ◽  
Symmetric Hyperbolic System ◽  
First Order ◽  
Initial Hypersurface ◽  
The Cauchy Problem ◽  
Data Subject ◽  
The Universe

Consideration is given to the Cauchy problem for perfect fluid space-times which evolve from an initial singularity of conformal type. The evolution equations for the conformally transformed, unphysical geometry are shown to be expressible as a first order symmetric hyperbolic system, albeit with a singular forcing term. It is concluded that the 3-metric on the initial hypersurface of the unphysical space-time constitutes the freely specifiable initial data. Subject to Penroses’s Weyl Curvature Hypothesis, according to which the Weyl tensor was initially zero, it follows that the physical space-time is Robertson–Walker. This may provide a basis for a new explanation for the large-scale isotropy of the universe.

scholarly journals Uniqueness issues for evolution equations with density constraints

2016 ◽  
Vol 26 (09) ◽  
pp. 1761-1783 ◽  
Author(s):  
Simone Di Marino ◽  
Alpár Richárd Mészáros
Keyword(s):  
Velocity Field ◽  
Evolution Equations ◽  
Planck Equation ◽  
Wasserstein Distance ◽  
First Order ◽  
Uniqueness Results ◽  
Monotonicity Assumption ◽  
Crowd Motion ◽  
The Given ◽  
Uniqueness Of A Solution

In this paper, we present some basic uniqueness results for evolution equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a monotonicity assumption: we prove the uniqueness of a solution for first-order systems modeling crowd motion with hard congestion effects, introduced recently by Maury et al. The monotonicity of the velocity field implies that the [Formula: see text]-Wasserstein distance along two solutions is [Formula: see text]-contractive, which in particular implies uniqueness. In the case of diffusive models, we prove the uniqueness of a solution passing through the dual equation, where we use some well-known parabolic estimates to conclude an [Formula: see text]-contraction property. In this case, by the regularization effect of the nondegenerate diffusion, the result follows even if the given velocity field is only [Formula: see text] as in the standard Fokker–Planck equation.

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