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11.
12.
We consider an inverse boundary problem for a general second order self-adjoint elliptic differential operator on a compact differential manifold with boundary. The inverse problem is that of the reconstruction of the manifold and operator via all but finite number of eigenvalues and traces on the boundary of the corresponding eigenfunctions of the operator. We prove that the data determine the manifold and the operator to within the group of the generalized gauge transformations. The proof is based upon a procedure of the reconstruction of a canonical object in the orbit of the group. This object, the canonical Schrödinger operator, is uniquely determined via its incomplete boundary spectral data. 相似文献
13.
Given a finite word u, we define its palindromic length |u|pal to be the least number n such that u=v1v2…vn with each vi a palindrome. We address the following open question: let P be a positive integer and w an infinite word such that |u|pal?P for every factor u of w. Must w be ultimately periodic? We give a partial answer to this question by proving that for each positive integer k, the word w must contain a k -power, i.e., a factor of the form uk. In particular, w cannot be a fixed point of a primitive morphism. We also prove more: for each pair of positive integers k and l, the word w must contain a position covered by at least l distinct k-powers. In particular, w cannot be a Sierpinski-like word. 相似文献
14.
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(Accepted May 14, 1998) 相似文献
15.
. We analyze a class of vector fields, called divergence‐measure fields. We establish the Gauss‐Green formula, the normal traces over subsets of
Lipschitz boundaries, and the product rule for this class of fields. Then we apply this theory to analyze entropy solutions of initial‐boundary‐value problems for hyperbolic conservation laws and to study the ways in which the
solutions assume their initial and boundary data. The examples of conservation laws include multidimensional scalar equations,
the system of nonlinear elasticity, and a class of systems with affine characteristic hypersurfaces. The analysis in also extends to .
(Accepted July 16, 1998) 相似文献
16.
Divergence-measure fields are extended vector fields, including vector fields inL
p
and vector-valued Radon measures, whose divergences are Radon measures. Such fields arise naturally in the study of entropy solutions of nonlinear conservation laws and other areas. In this paper, a theory of divergence-measure fields is presented and analyzed, in which normal traces, a generalized Gauss-Green theorem, and product rules, among others, are established. Some applications of this theory to several nonlinear problems in conservation laws and related areas are discussed. In particular, with the aid of this theory, we prove the stability of Riemann solutions, which may contain rarefaction waves, contact discontinuities, and/or vacuum states, in the class of entropy solutions of the Euler equations for gas dynamics.Dedicated to Constantine Dafermos on his 60th birthday 相似文献
17.
18.
Raimund Bürger Hermano Frid Kenneth H. Karlsen 《Journal of Mathematical Analysis and Applications》2007,326(1):108-120
We study a zero-flux type initial-boundary value problem for scalar conservation laws with a genuinely nonlinear flux. We suggest a notion of entropy solution for this problem and prove its well-posedness. The asymptotic behavior of entropy solutions is also discussed. 相似文献
19.
The global unique solvability is proved for the Navier–Stokes equations of compressible fluids for the one-dimensional spiral
flows between two circular cylinders. The zero shear viscosity limit μ→ 0 is justified. The value O(μα), 0 < α < 1/2, is established for the boundary layer thickness.
Received: 11 December 1998 / Accepted: 9 June 1999 相似文献
20.
We prove the asymptotic stability of nonplanar two-states Riemann solutions in BGK approximations of a class of multidimensional systems of conservation laws. The latter consists of systems whose flux-functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. The asymptotic stability to which the main result refers is in the sense of the convergence as t→∞ in of the space of directions ζ=x/t. That is, the solution z(t,x,ξ) of the perturbed Cauchy problem for the corresponding BGK system satisfies as t→∞, in , where R(ζ) is the self-similar entropy solution of the two-states nonplanar Riemann problem for the system of conservation laws. 相似文献