Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems with One Weakly Linearly Degenerate Characteristic

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...     

对角型拟线性双曲组整体经典解的渐近行为

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.     

具常重特征的非齐次拟线性双曲组的整体弱间断解

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.     

拟线性双曲组在半有界初始轴上的柯西问题整体经典解的渐近性态

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.     

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

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.     

Initial Value Problem for General Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity

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.     

初值的导数具有紧支集的对角形双曲组Cauchy问题经典解的整体存在唯一性

本文研究了初值导数具有紧支集的对角形严格双曲组Cauchy问题在t>0上的经典解的整体存在唯一性,以及在最大特征的决定区域内的较一般的非严格双曲组的初值是在x≥0半轴上给定的,并且初值具有紧支集的Cauchy问题的经典解的整体存在唯一性.文中主要使用了特征线方法和解的一致先验估计方法.     

三步完全可化约拟线性双曲组型方程组的整体经典解

本文对三步完全可化约拟线性双曲型方程组的整体经典解进行讨论，得到了整体经典解的存在性．这一结果说明非线性特征向量也可能引发奇性．     

一阶非齐次拟线性双曲组的柯西问题整体经典解的存在性

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．     

Asymptotic Behavior of Solutions to a Class of Semilinear Parabolic Equations with Boundary Degeneracy

This paper concerns the asymptotic behavior of solutions to one-dimensional semilinear parabolic equations with boundary degeneracy both in bounded and unbounded intervals. For the problem in a bounded interval, it is shown that there exist both nontrivial global solutions for small initial data and blowing-up solutions for large one if the degeneracy is not strong. Whereas in the case that the degeneracy is strong enough, the nontrivial solution must blow up in a finite time. For the problem in an unbounded interval, blowing-up theorems of Fujita type are established. It is shown that the critical Fujita exponent depends on the degeneracy of the equation and the asymptotic behavior of the diffusion coefficient at infinity, and it may be equal to one or infinity. Furthermore, the critical case is proved to belong to the blowing-up case.     

Global Existence of Classical Solution with Small Initial Total Variation for Quasilinear Linearly Degenerate Hyperbolic Systems

In this paper, the author proves the global existence of classical solution to the Cauchy problem with slowly decaying initial data with small initial total variation for general first order quasilinear linearly degenerate hyperbolic systems. This generalizes the corresponding result of A.Bressan for initial data with compact support.     

Global Exact Boundary Controllability for General First-Order Quasilinear Hyperbolic Systems

For general first-order quasilinear hyperbolic systems, based on the analysis of simple wave solutions along characteristic trajectories, the global two-sided exact boundary controllability is achieved in a relatively short controlling time.     

Existence and Asymptotic Behavior of Radially Symmetric Solutions to a Semilinear Hyperbolic System in Odd Space Dimensions

This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t→-∞in the energy norm, and to show it has a free profile as t→ ∞. Our approach is based on the work of [11]. Namely we use a weighted L∞norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.     

Fujita型反应扩散方程组整体解的存在性、非存在性与渐近性质

本文研究 Ｆｕｊｉｔａ型反应扩散方程组的初值问题：ｕｔ－△ｕ＝ａ１ｕ~α１－１ｕ＋ｂ１ｖ~β１－１ｖ,ｖｔ－△ｖ＝ａ２ｕ~α２－１ｕ＋ｂ２ｖ~β２－１ｖ,ｕ（Ｘ,０）＝ｕ０（Ｘ）,Ｖ（Ｘ,０）＝Ｖ０（Ｘ）,（Ｘ,ｔ）Ｒ~Ｎ ｘ Ｒ~＋,其中 ａｉ,ｂｉ≥ ０, αｉ,βｉ≥ １（ｉ＝ １,２）,给出了非负整体 Ｌ~ｐ解与古典解存在性与非存在性的一系列充分条件,并讨论了解的渐近性质．本文所用方法和所得结果与已有的工作［１－４］,有很大的不同,不但在某些方面推广了［１－５］,而且从某些方面改进了［１］的结果。     

The Asymptotic Behavior of Global Smooth Solutions to the Macroscopic Models for Semiconductors

The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem. First, it is proved that the solutions to these two systems converge to the unique stationary solution time asymptotically without the smallness assumption on doping profile. Then, very sharp estimates on the smooth solutions, independent of the relaxation time, are obtained and used to establish the zero relaxation limit.     

线性退化的严格双曲组具慢衰减初值的Cauchy问题的经典解

该文给出了线性退化的严格双曲组具慢衰减及小全变差初值的Cauchy问题的经典解的整体存在唯一性. 这个结果进一步推广了A Bressan的相关结果     

Geometry of quasilinear hyperbolic systems with characteristic fields of constant multiplicity

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.     

One-Sided Exact Boundary Null Controllability of Entropy Solutions to a Class of Hyperbolic Systems of Conservation Laws with Characteristics with Constant Multiplicity

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.     

Existence and Nonexistence of Global Classical Solutions to Porous Medium and Plasma Equations with Singular Sources

Let Ω be a bounded or unbounded domain in R^n. The initial-boundary value problem for the porous medium and plasma equation with singular terms is considered in this paper. Criteria for the appearance of quenching phenomenon and the existence of global classical solution to the above problem are established. Also, the life span of the quenching solution is estimated or evaluated for some domains.