Characteristics Of Constant Multiplicity Research Articles

Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws

In this paper, we study the local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws with characteristics of constant multiplicity. We prove the two-sided boundary controllability, the one-sided boundary controllability and the two-sided boundary controllability with fewer controls, by applying the strategy used in [T. Li and L. Yu, J. Math. Pures et Appl. 107 (2017) 1–40; L. Yu, Chinese Ann. Math., Ser. B (To appear)]. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions, and on some further properties of both ε-approximate front tracking solutions and limit solutions.

Conditions of hyperbolicity of linear differentiable systems with constant multiplicity

Let h be a system with characteristics of constant multiplicity. We prove that if there exists an operator A′ such that h∘A′ has diagonal principal part and admits a good decomposition, then h must satisfy the Levi conditions.

Stability of multidimensional viscous shocks for symmetric systems with variable multiplicities

We establish long-time stability of multi-dimensional viscous shocks of a general class of symmetric hyperbolic--parabolic systems with variable multiplicities, notably including the equations of compressible magnetohydrodynamics (MHD) in dimensions $d\ge 2$. This extends the existing result established by K. Zumbrun for systems with characteristics of constant multiplicity to the ones with variable multiplicity, yielding the first such a stability result for (fast) MHD shocks. At the same time, we are able to drop a technical assumption on structure of the so--called glancing set that was necessarily used in previous analyses. The key idea to the improvements is to introduce a new simple argument for obtaining a $L^1\to L^p$ resolvent bound in low--frequency regimes by employing the recent construction of degenerate Kreiss' symmetrizers by O. Gu\`es, G. M\'etivier, M. Williams, and K. Zumbrun. Thus, at the low-frequency resolvent bound level, our analysis gives an alternative to the earlier pointwise Green's function approach of K. Zumbrun. High--frequency solution operator bounds have been previously established entirely by nonlinear energy estimates.

Sur la monodromie du problème de Cauchy ramifié

In this paper, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution's monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam.

Monodromie du problème de Cauchy ramifié

In this Note, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution's monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam. To cite this article: R. Camalès, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 639–642.

Ramification non abélienne

In this work, we study the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. We show that the theorems of Hamada-Leray-Wagschal, Hamada-Takeuchi and Leichtnam can be reduce to an unique integro-differential equation where the datas are holomorphic on the universal covering of an open set of C 2 and holomorphic in an neighbourhood of the origin of C n+1 with respect the other variables.

Uniqueness of the cauchy problem for elliptic operators with fourfold characteristics of constant multiplicity

We are concerned with the uniqueness of the Cauchy problem for elliptic differential operators. This topic has a long history. In 1939, T. Carleman obtained the uniqueness result for the first order systems with simple characteristics in two independent variables. A. P. Calderon extended this result to any dimensional case by using the calculus of singular integral operators. For multiple characteristic cases, S. Mizohata proved the uniqueness for the Cauchy problem for elliptic operators with double characteristics of constant multiplicity. Later, A. P. Calderon unified these results for operators with characteristics of constant multiplicity, which are at most double while the real ones are at most simple. K.Watanabe has shown that the uniqueness for elliptic operators holds if they have at most triple characteristics of constant multiplicity. As for negative results, in 1961, A. Plis gave the nonuniqueness result for an elliptic operator having sixfold characteristics of constant multiplicity. In his article, he constructed two C{sup {infinity}} functions {alpha}(x, t) and u(x, t) defined in a neighborhood of the origin in R{sup 2} such that and suppu {contained_in} (t {ge} 0), and 0 {element_of} suppu. 25 refs.

On the partially microlocal hypoellipticity for a class of totally characteristic operators with characteristics of constant multiplicity

In this paper, I study the microlocal hypoellipticity for a class of totally characteristic operators (1.1). My main result is as follows:

Anisotropic Operators with Characteristics of Constant Multiplicity

Mathematische NachrichtenVolume 124, Issue 1 p. 199-216 Article Anisotropic Operators with Characteristics of Constant Multiplicity Michael Lorenz, Michael Lorenz Akademie der Wissenschaften der DDR Karl-Weierstraß-Institut für Mathematik DDR - 1086 Berlin Mohrenstraße 39Search for more papers by this author Michael Lorenz, Michael Lorenz Akademie der Wissenschaften der DDR Karl-Weierstraß-Institut für Mathematik DDR - 1086 Berlin Mohrenstraße 39Search for more papers by this author First published: 1985 https://doi.org/10.1002/mana.19851240113Citations: 4AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume124, Issue11985Pages 199-216 RelatedInformation

Wave fronts of solutions of boundary-value problems for symmetric hyperbolic systems II. Systems with characteristics of constant multiplicity

Wave fronts of solutions of boundary-value problems for symmetric hyperbolic systems II. Systems with characteristics of constant multiplicity

The Levi-Lax condition for partial differential equations with real characteristics of constant multiplicity

The object of this paper is to show that the Levi-Lax condition is necessary and sufficient for the Cauchy problem to be well-posed.

Uniqueness of solutions of the Cauchy problem for linear partial differential equations with characteristics of constant multiplicity

Uniqueness of solutions of the Cauchy problem for linear partial differential equations with characteristics of constant multiplicity