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1.
Formation of Singularities for Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity 下载免费PDF全文
Libin Wang 《偏微分方程(英文版)》2003,16(3):240-254
In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity(> 1), under the assumptions that there is a genuinely nonlinear simple characteristic and the initial data possess certain decaying properties, the blow-up result is obtained for the C¹ solution to the Cauchy problem. 相似文献
2.
We study the well-posedness of the mixed problem for hyperbolic equations with constant coefficients and with characteristics of variable multiplicity. We single out a class of higher-order hyperbolic operators with constant coefficients and with characteristics of variable multiplicity, for which we obtain a generalization of the Sakamoto conditions for the well-posedness of the mixed problem in L 2. 相似文献
3.
The paper is devoted to the study of the well-posedness of mixed problems for hyperbolic equations with constant coefficients
and characteristics of variable multiplicity. The authors distinguish a class of higher-order hyperbolic operators with constant
coefficients and characteristics of variable multiplicity for which a generalization of the Sakamoto L
2-well-posedness of the mixed problem is obtained.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 85–98, 2006. 相似文献
4.
《Applied Mathematics Letters》2003,16(2):143-146
In this note, we generalize the recent result on L1 well-posedness theory for strictly hyperbolic conservation laws to the nonstrictly hyperbolic system of conservation laws whose characteristics are with constant multiplicity. 相似文献
5.
Initial Value Problem for General Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity 下载免费PDF全文
The authors consider the global existence and the blow-up phenomenon of classical solutions with small amplitude to the Cauchy problem for general quasilinear hyperbolic systems with characteristics with constant multiplicity and given some applications. 相似文献
6.
《Journal de Mathématiques Pures et Appliquées》2002,81(7):603-640
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. 相似文献
7.
T. E. Gureev 《Journal of Mathematical Sciences》1995,73(6):638-656
It is shown that the characteristics of the Maxwell operator in a resonator with a smooth inhomogeneous anisotropic filler
have constant multiplicity if and only if the matrices of dielectric permittivity and magnetic permeability are connected
by the relation ε≡f μ, where f is a scalar-valued function. When ε≡f μ and the boundary is smooth and ideally conducting,
the coefficient of λ2 in the asymptotic expansion of the distribution function of the eigenvalues of the Maxwell operator turns out to be zero.
When the multiplicity of the characteristics is variable, this coefficient can be either zero or nonzero. Bibliography: 22
titles.
Translated fromProblemy Matematicheskogo Analiza, No. 13, 1992, pp. 48–79. 相似文献
8.
I. N. Shchitov 《Differential Equations》2014,50(5):667-676
We construct asymptotic expansions of solutions of the Cauchy problem with rapidly oscillating initial data for hyperbolic systems with constant coefficients and with characteristics of a variable multiplicity. By way of example, we consider the system of Maxwell equations. 相似文献
9.
本文得到两个结果:首先证明尺度因子m与重数r的乘积为奇数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)(μ∈N)的正交向量小波系统的不存在性;其次证明尺度因子m=3,重数r为偶数时,具有相同对称/反对称中心1/2(1+μ+μ/m-1)的正交平衡向量小波系统的不存在性,这里N是正整数集合. 相似文献
10.
We classify hypersurfaces of the hyperbolic space ?n+1(c) with constant scalar curvature and with two distinct principal curvatures. Moreover, we prove that if Mn is a complete hypersurfaces with constant scalar curvature n(n ? 1) R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n? 1, then R ≥ c. Additionally, we prove two rigidity theorems for such hypersurfaces. 相似文献
11.
Lei YU 《数学年刊B辑(英文版)》2018,39(6):947-962
This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathématiques Pures et Appliquées, 2016.] for a class of strictly hyperbolic systems of conservation laws. 相似文献
12.
This paper considers the Cauchy problem with a kind of non-smooth initial data for general inhomogeneous quasilinear hyperbolic systems with characteristics with constant multiplicity. Under the matching condition, based on the refined fomulas on the decomposition of waves, we obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution to the Cauchy problem. 相似文献
13.
Fangtong Wu 《偏微分方程(英文版)》1998,11(2):151-162
In this paper we consider the propagation of microlocal regularity near constant multiple characteristic or a real solution u ∈ H^s (s > m + max{μ, 2} + \frac{n}{2})or non-linear partial differential equation F(x, u,…, ∂^βu,…)_{(|β|≤m)} = 0 We will prove that the microlocal regularity ncar constant multiple characteristic of the solution u will propagate along bicharacteristic with constant multiplicity μ and have loss of smoothness up to order μ - 1 under Levi condition. 相似文献
14.
Renaud Camalès 《Comptes Rendus Mathematique》2002,334(8):639-642
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. 相似文献
15.
Vladimir Schuchman 《Journal of Differential Equations》1983,48(3):313-325
This paper contains a proof of γn(χ) correctness of the noncharacteristic Cauchy problem for nonstrictly hyperbolic equations with analytic coefficients under the condition that its characteristic roots are smooth and under some additional assumptions on the lower-order terms. There are two extreme cases: (1) . In this case condition (0.6) is “void,” and we do not require conditions on Ps for s < m. For this case, see [3, 8]. (2) Case of constant multiplicity of characteristic roots and χ = +∞. In this case condition (0.6) implies conditions on Ps, where s = m, m ? 1,…, m ? r + 1, i.e., up to the same order as the necessary condition for C∞-correctness [2]. Recall that in the case of equations with characteristics of constant multiplicity condition (0.6) (Levi's condition in this case) for χ = ∞ is necessary [2, 4] and sufficient [1] for C∞-correctness. 相似文献
16.
《偏微分方程通讯》2013,38(9-10):2007-2030
ABSTRACT This paper is concerned with strong resonant problems for nonlinear elliptic Dirichlet BVPs. Classifying the decay rates of the nonlinearity at infinity and using a Morse theoretical approach developed in our earlier work, we are able to establish several multiplicity results of positive and sign-changing solutions. 相似文献
17.
Wen-Rong Dai 《Journal of Mathematical Analysis and Applications》2007,327(1):188-202
In this paper, we study the regularity of the eigenvalues and eigenvectors and the existence of normalized coordinates for quasilinear hyperbolic systems with characteristic fields of constant multiplicity. We prove that the eigenvalues and eigenvectors of the system have the same regularity as the coefficients of the system. On the other hand, we show that, for the quasilinear hyperbolic system of conservation laws with characteristic fields of constant multiplicity, the normalized coordinates exist on the domain under consideration. 相似文献
18.
WANG Zaihong 《数学年刊B辑(英文版)》2000,21(4):479-488
This paper deals with the existence and multiplicity of periodic solutions of Duffing equations
. The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided thatg(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property. 相似文献
19.
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:{-△pu-△qu=│u│^p*-2u+μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^*=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ (0, μ0), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem. 相似文献
20.
For two-dimensional Coxeter systems with arbitrary multiplicities, a basis of the module of quasi-invariants over the invariants is explicitly constructed. It is proved that the basis thus obtained consists of m-harmonic polynomials. Hence this generalizes earlier results of Veselov and the author for systems of constant multiplicity. 相似文献