Shock-Wave Solutions of the Einstein Equations with Perfect Fluid Sources: Existence and Consistency by a Locally Inertial Glimm Scheme PDF Download
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Author: Jeff Groah
Publisher: American Mathematical Soc.
ISBN: 082183553X
Category : Mathematics
Languages : en
Pages : 98
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Book Description
Demonstrates the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation.
Author: Jeff Groah
Publisher: American Mathematical Soc.
ISBN: 082183553X
Category : Mathematics
Languages : en
Pages : 98
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Book Description
Demonstrates the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation.
Author: Jeffrey Groah
Publisher: Springer Science & Business Media
ISBN: 0387446028
Category : Mathematics
Languages : en
Pages : 157
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Book Description
This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The author is a well regarded expert in this area.
Author: Sylvie Benzoni-Gavage
Publisher: Springer Science & Business Media
ISBN: 3540757120
Category : Mathematics
Languages : en
Pages : 1117
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Book Description
This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.
Author: Eric T. Sawyer
Publisher: American Mathematical Soc.
ISBN: 0821838261
Category : Mathematics
Languages : en
Pages : 176
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Book Description
This mathematical monograph is a study of interior regularity of weak solutions of second order linear divergence form equations with degenerate ellipticity and rough coefficients. The authors show that solutions of large classes of subelliptic equations with bounded measurable coefficients are H lder continuous. They present two types of results f
Author: Nicole Bopp
Publisher: American Mathematical Soc.
ISBN: 0821836234
Category : Mathematics
Languages : en
Pages : 250
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Book Description
Intends to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces.
Author: Jeff Groah
Publisher:
ISBN: 9781470404147
Category : Conservation laws
Languages : en
Pages : 84
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Book Description
Introduction Preliminaries The fractional step scheme The Riemann problem step The ODE step Estimates for the ODE step Analysis of the approximate solutions The elimination of assumptions Convergence.
Author: Joachim Krieger
Publisher: American Mathematical Soc.
ISBN: 0821838776
Category : Mathematics
Languages : en
Pages : 96
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Book Description
Presents a study of Wave Maps from ${\mathbf{R}}^{2+1}$ to the hyperbolic plane ${\mathbf{H}}^{2}$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some $H^{1+\mu}$, $\mu>0$.
Author: John M. Lee
Publisher: American Mathematical Soc.
ISBN: 0821839152
Category : Mathematics
Languages : en
Pages : 98
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Book Description
"Volume 183, number 864 (end of volume)."
Author: Viorel Barbu
Publisher: American Mathematical Soc.
ISBN: 0821838741
Category : Mathematics
Languages : en
Pages : 146
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Book Description
In order to inject dissipation as to force local exponential stabilization of the steady-state solutions, an Optimal Control Problem (OCP) with a quadratic cost functional over an infinite time-horizon is introduced for the linearized N-S equations. As a result, the same Riccati-based, optimal boundary feedback controller which is obtained in the linearized OCP is then selected and implemented also on the full N-S system. For $d=3$, the OCP falls definitely outside the boundaries of established optimal control theory for parabolic systems with boundary controls, in that the combined index of unboundedness--between the unboundedness of the boundary control operator and the unboundedness of the penalization or observation operator--is strictly larger than $\tfrac{3}{2}$, as expressed in terms of fractional powers of the free-dynamics operator. In contrast, established (and rich) optimal control theory [L-T.2] of boundary control parabolic problems and corresponding algebraic Riccati theory requires a combined index of unboundedness strictly less than 1. An additional preliminary serious difficulty to overcome lies at the outset of the program, in establishing that the present highly non-standard OCP--with the aforementioned high level of unboundedness in control and observation operators and subject, moreover, to the additional constraint that the controllers be pointwise tangential--be non-empty; that is, it satisfies the so-called Finite Cost Condition [L-T.2].
Author: Sławomir Kołodziej
Publisher: American Mathematical Soc.
ISBN: 082183763X
Category : Mathematics
Languages : en
Pages : 82
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Book Description
We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.
