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71.
Gang Xu 《Journal of Differential Equations》2008,245(11):3389-3432
In this paper, we are concerned with the global existence and stability of a steady transonic conic shock wave for the symmetrically perturbed supersonic flow past an infinitely long conic body. The flow is assumed to be polytropic, isentropic and described by a steady potential equation. Theoretically, as indicated in [R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, 1948], it follows from the Rankine-Hugoniot conditions and the entropy condition that there will appear a weak shock or a strong shock attached at the vertex of the sharp cone in terms of the different pressure states at infinity behind the shock surface, which correspond to the supersonic shock and the transonic shock respectively. In the references [Shuxing Chen, Zhouping Xin, Huicheng Yin, Global shock wave for the supersonic flow past a perturbed cone, Comm. Math. Phys. 228 (2002) 47-84; Dacheng Cui, Huicheng Yin, Global conic shock wave for the steady supersonic flow past a cone: Polytropic case, preprint, 2006; Dacheng Cui, Huicheng Yin, Global conic shock wave for the steady supersonic flow past a cone: Isothermal case, Pacific J. Math. 233 (2) (2007) 257-289] and [Zhouping Xin, Huicheng Yin, Global multidimensional shock wave for the steady supersonic flow past a three-dimensional curved cone, Anal. Appl. 4 (2) (2006) 101-132], the authors have established the global existence and stability of a supersonic shock for the perturbed hypersonic incoming flow past a sharp cone when the pressure at infinity is appropriately smaller than that of the incoming flow. At present, for the supersonic symmetric incoming flow, we will study the global transonic shock problem when the pressure at infinity is appropriately large. 相似文献
72.
We obtain estimates on the continuous dependence on the coefficient for second-order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et al., Jakobsen and Karlsen, and Gripenberg to problems with more general boundary conditions and domains. A new feature here is that we account for the dependence on the boundary conditions. As one application of our continuous dependence results, we derive for the first time the rate of convergence for the vanishing viscosity method for such problems. We also derive new explicit continuous dependence on the coefficients results for problems involving Bellman-Isaacs equations and certain quasilinear equation. 相似文献
73.
Serguei Norine 《Combinatorica》2008,28(1):89-98
We characterize Pfaffian graphs in terms of their drawings in the plane. We generalize the techniques used in the proof of
this characterization, and prove a theorem about the numbers of crossings in T-joins in different drawings of a fixed graph. As a corollary we give a new proof of a theorem of Kleitman on the parity of
crossings in drawings of K
2j+1 and K
2j+1,2k+1.
Partially supported by NSF grants DMS-0200595 and DMS-0701033. 相似文献
74.
Rink 《Journal of Nonlinear Science》2008,12(5):479-504
Summary. This paper considers the famous Fermi-Pasta-Ulam (FPU) lattice with periodic boundary conditions and quartic nonlinearities.
Due to special resonances and discrete symmetries, the Birkhoff normal form of this Hamiltonian system is Liouville integrable.
The normal form equations can easily be solved if the number of particles in the lattice is odd, but if the number of particles
is even, several nontrivial phenomena occur. In the latter case we observe that the phase space of the normal form is decomposed
in invariant subspaces that describe the interaction between the Fourier modes with wave number j and the Fourier modes with wave number n / 2-j . We study how the level sets of the integrals of the normal form foliate these invariant subspaces. The integrable foliations
turn out to be singular and the method of singular reduction shows that the normal form has invariant pinched tori and monodromy.
Monodromy is an obstruction to the existence of global action-angle variables. The pinched tori are interpreted as homoclinic
and heteroclinic connections between traveling waves. Thus we discover a class of solutions of the normal form which can be
described as direction-reversing traveling waves. The relation between the FPU lattice and its Birkhoff normal form can be
understood from KAM theory and approximation theory. This explains why we observe the impact of the direction-reversing traveling
waves numerically as a relaxation oscillation in the original FPU system. 相似文献
75.
76.
A hyperbolic problem with volume constraint is investigated by means of a minimizing method called the discrete Morse flow. A weak solution is introduced in a constructive way and results of numerical computations are shown. 相似文献
77.
Quadratic alternative superalgebras are introduced and their super-identities and central functions on one odd generator are described. As a corollary, all multilinear skew-symmetric identities and central polynomials of octonions are classified. 相似文献
78.
This paper deals with some Sobolev-type inequalities with weights that were proved by Maz’ya in 1980 and by Caffarelli–Kohn–Nirenberg in 1984. 相似文献
79.
We study tail probabilities of the suprema of Lévy processes with subexponential or exponential marginal distributions over compact intervals. Several of the processes for which the asymptotics are studied here for the first time have recently become important to model financial time series. Hence our results should be important, for example, in the assessment of financial risk. 相似文献
80.
We prove a local in time smoothing estimate for a magnetic Schrödinger equation with coefficients growing polynomially at spatial infinity. The assumptions on the magnetic field are gauge invariant and involve only the first two derivatives. The proof is based on the multiplier method and no pseudodifferential techniques are required. 相似文献