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1.
For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.  相似文献   

2.
本文考察了弱线性退化的一阶非齐次拟线性严格双曲组具有小初值的柯西问题.在非齐次项满足匹配条件的假设下,给出了精细的波的分解公式,利用这些公式,证明了整体C1解的存在唯一性和稳定性.  相似文献   

3.
本文考察了弱线性退化的一阶非齐次拟线性严格双曲组具有小初值的柯西问题.在非齐次项满足匹配条件的假设下,给出了精细的波的分解公式,利用这些公式,证明了整体C1解的存在唯一性和稳定性.  相似文献   

4.
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   

5.
In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate (1 + t)^-u, provided that the initial data decay with the rate (1 + x)^-(l+u) (resp. (1 - x)^-(1+u)) as x tends to +∞ (resp. -∞), where u is a positive constant.  相似文献   

6.
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   

7.
In this paper, we consider Cauchy problem for general first order inho- mogeneous quasilinear strictly hyperbolic systems. Under the matching condition, we first give an estimate on inhomogeneous terms. By this estimate, we obtain the asymptotic behaviour for the life-span of C¹ solutions with “slowly” decaying and small initial data and prove that the formation of singularity is due to the envelope of characteristics of the same family.  相似文献   

8.
In this paper, we study the Cauchy problem for quasilinear hyperbolic system with a kind of non‐smooth initial data. Under the assumption that the initial data possess a suitably small bounded variation norm, a necessary and sufficient condition is obtained to guarantee the existence and uniqueness of global weak discontinuous solution. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

9.
The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems. Under the assumption that the system is weakly dissipative, Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch. Rational Mech. Anal., Vol. 169, 2003, pp. 89–117). The aim of this paper is to give a completely different proof of this result with slightly different assumptions.  相似文献   

10.
This paper deals with the asymptotic behavior of global classical solutions to quasilinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. On the basis of global existence and uniqueness of C^1 solution, we prove that the solution to the Cauchy problem approaches a combination of C^1 traveling wave solutions when t tends to the infinity.  相似文献   

11.
In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.  相似文献   

12.
For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissi...  相似文献   

13.
In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {(t, x) | t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.  相似文献   

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