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1.
The second law of thermodynamics and stability 总被引:10,自引:0,他引:10
C. M. Dafermos 《Archive for Rational Mechanics and Analysis》1979,70(2):167-179
2.
Constantine M. Dafermos 《Ricerche di matematica》2006,55(1):79-92
Abstract The paper employs the method of characteristics to show that continuous solutions of scalar conservation laws do not incur
entropy production and to recover, in a direct and elementary way the (known) properties of solutions to the Hunter-Saxton
equation.
Keywords: Balance laws, Characteristics, Hunter-Saxton equation
Mathematics Subject Classification (2000): 35L65, 35Q58 相似文献
3.
4.
This paper shows that market equilibrium problems of production may generally be modelled as equilibrium flow problems in networks and that their equilibrium conditions can be visualized as a variational inequality. This connection would allow us to transplant directly elements of the well-developed theory of equilibrium flow in networks to the theory of market equilibrium. 相似文献
5.
6.
Constantine M. Dafermos 《偏微分方程通讯》2013,38(7):1274-1286
Physically admissible, global BV solutions are constructed to the Cauchy problem for the equations of one-dimensional, nonlinear viscoelasticity of the Boltzmann type. The required BV bounds are derived with the help of energy estimates, in conjunction with a change of variables that redistributes the damping on an equitable basis among the equations of the system, thus exposing the dissipative effect of viscosity on the variation of solutions. 相似文献
7.
We consider solutions to the linear wave equation □g? = 0 on a (maximally extended) Schwarzschild spacetime with parameter M > 0, evolving from sufficiently regular initial data prescribed on a complete Cauchy surface Σ, where the data are assumed only to decay suitably at spatial infinity. (In particular, the support of ? may contain the bifurcate event horizon.) It is shown that the energy flux F(??) of the solution (as measured by a strictly timelike T? that asymptotically matches the static Killing field) through arbitrary achronal subsets ?? of the black hole exterior region satisfies the bound F(??) ≤ C E(v + u), where v and u denote the infimum of the Eddington‐Finkelstein advanced and retarded time of ??, v+ denotes max{1, v}, and u+ denotes max{1, u}, where C is a constant depending only on the parameter M, and E depends on a suitable norm of the solution on the hypersurface t ? u + v = 1. (The bound applies in particular to subsets ?? of the event horizon or null infinity.) It is also shown that ? satisfies the pointwise decay estimate |?| ≤ C Ev in the entire exterior region, and the estimates |r?| ≤ CR?E(1 + |u|)?1/2 and |r1/2?| ≤ CR?Eu in the region {r ≥ R?} ∩ J+(Σ) for any R? > 2M. The estimates near the event horizon exploit an integral energy identity normalized to local observers. This estimate can be thought to quantify the celebrated red‐shift effect. The results in particular give an independent proof of the classical result |?| ≥ C E of Kay and Wald without recourse to the discrete isometries of spacetime. © 2009 Wiley Periodicals, Inc. 相似文献
8.
Gui-Qiang Chen Constantine M. Dafermos Marshall Slemrod Dehua Wang 《Communications in Mathematical Physics》2007,271(3):635-647
A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-dimensional Euler equations
for steady irrotational flows that may contain stagnation points. Only crude estimates are required for establishing compactness.
It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points
over an obstacle, such as an airfoil, may be realized as limits of sequences of strictly subsonic flows. Furthermore, sonic-subsonic
flows may be constructed from approximate solutions. The compactness framework is then extended to self-similar solutions
of the Euler equations for unsteady irrotational flows. 相似文献
9.
A well-known open problem in general relativity, dating back to 1972, has been to prove Price’s law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation
flux through the event horizon and null infinity with respect to appropriately normalized advanced and retarded time coordinates.
It is intimately related both to astrophysical observations of black holes and to the fate of observers who dare cross the
event horizon. In this paper, we prove a well-defined (upper bound) formulation of Price’s law for the collapse of a self-gravitating
scalar field with spherically symmetric initial data. We also allow the presence of an additional gravitationally coupled
Maxwell field. Our results are obtained by a new mathematical technique for understanding the long-time behavior of large
data solutions to the resulting coupled non-linear hyperbolic system of p.d.e.’s in 2 independent variables. The technique
is based on the interaction of the conformal geometry, the celebrated red-shift effect, and local energy conservation; we
feel it may be relevant for the problem of non-linear stability of the Kerr solution. When combined with previous work of
the first author concerning the internal structure of charged black holes, which had assumed the validity of Price’s law, our results can be applied to the strong cosmic censorship conjecture for the Einstein-Maxwell-real
scalar field system with complete spacelike asymptotically flat spherically symmetric initial data. Under Christodoulou’s
C0-formulation, the conjecture is proven to be false. 相似文献
10.
An iterative scheme for variational inequalities 总被引:1,自引:0,他引:1
Stella Dafermos 《Mathematical Programming》1983,26(1):40-47
In this paper we introduce and study a general iterative scheme for the numerical solution of finite dimensional variational
inequalities. This iterative scheme not only contains, as special cases the projection, linear approximation and relaxation
methods but also induces new algorithms. Then, we show that under appropriate assumptions the proposed iterative scheme converges
by establishing contraction estimates involving a sequence of norms in En induced by symmetric positive definite matrices Gm. Thus, in contrast to the above mentioned methods, this technique allows the possibility of adjusting the norm at each step
of the algorithm. This flexibility will generally yield convergence under weaker assumptions. 相似文献