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

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

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.

scholarly journals Second-order type-changing evolution equations with first-order intermediate equations

2008 ◽  
Vol 244 (2) ◽  
pp. 242-273 ◽  
Author(s):  
Jeanne Clelland ◽  
Marek Kossowski ◽  
George R. Wilkens
Keyword(s):  
Evolution Equations ◽  
Order Type ◽  
Second Order ◽  
First Order

scholarly journals Existence Theorem for Noninstantaneous Impulsive Evolution Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Gul I Hina Aslam ◽  
Amjad Ali ◽  
Maimona Rafiq
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Constructive Theory ◽  
First Order ◽  
Linear Evolution ◽  
Semilinear Problems ◽  
Variational Structure ◽  
Linear Evolution Equation ◽  
Variational Form ◽  
Impulsive Evolution Equations

In this note, the variational form of the classical Lax–Milgram theorem is used for the divulgence of variational structure of the first-order noninstantaneous impulsive linear evolution equation. The existence and uniqueness of the weak solution of the problem is obtained. In future, this constructive theory can be used for the corresponding semilinear problems.

scholarly journals Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Methods

2021 ◽  
Author(s):  
Andreas Dedner ◽  
Robert Klöfkorn
Keyword(s):  
Partial Differential Equations ◽  
Discontinuous Galerkin ◽  
User Interfaces ◽  
Discontinuous Galerkin Methods ◽  
Evolution Equations ◽  
Nonlinear Partial Differential Equations ◽  
Galerkin Methods ◽  
First Order ◽  
Wide Range ◽  
Dg Method

AbstractThis paper discusses a Python interface for the recently published Dune-Fem-DG module which provides highly efficient implementations of the discontinuous Galerkin (DG) method for solving a wide range of nonlinear partial differential equations (PDEs). Although the C++ interfaces of Dune-Fem-DG are highly flexible and customizable, a solid knowledge of C++ is necessary to make use of this powerful tool. With this work, easier user interfaces based on Python and the unified form language are provided to open Dune-Fem-DG for a broader audience. The Python interfaces are demonstrated for both parabolic and first-order hyperbolic PDEs.

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