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		题名	作者	年代	出处	被引量
	1	ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATION显示文摘The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler- Poisson-Darboux equation. The entropy kernel is only Holder continuous and its regularity is carefully inversti- gated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of eatropy flux-splittings coincides with the set of entropies-entropy fluxes. There results imply the existence of a flux-splitting consistent with all of the entropy inequalities.	CHENGUIQIANG P.G.LEFLOCH	2001	Chinese Annals of Mathematics,Series B2001，22，2：	0
	2	DISCONTINUOUS SOLUTIONS IN L~∞ FOR HAMILTON-JACOBI EQUATIONS显示文摘An approach is introduced to construct global discontinuous solutions in L∞ for Hamilton-Jacobi equations. This approach allows the initial data only in L∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discontinuous solutions in L∞. The existence of global discontinuous solutions in L∞ is established. These solutions in L∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed toexamine the L∞ stability of our L∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated.	CHENGUIQIANG SUBo	2000	Chinese Annals of Mathematics,Series B2000，21，2：	0

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