This paper extends symbolic dynamics to general cases. Some chaotic properties and applications of the general symbolic dynamics (Σ(X), σ) and its special cases are discussed, where X is a separable metric space.
Many important results have been got in the study of application of the com pactness theory in partial differential equations. But as far as we know, there are mainly two application ways: One is the analysis of Tarta...Many important results have been got in the study of application of the com pactness theory in partial differential equations. But as far as we know, there are mainly two application ways: One is the analysis of Tartar or the static structure of the Young measure; another is the analysis of Diperna of the展开更多
the existence behavior of solution has been considered in many papers. Unfortunately there are no results to the asymptotic behavior of Cauchy problem with great data. In this report, we mainly consider the asymptotic...the existence behavior of solution has been considered in many papers. Unfortunately there are no results to the asymptotic behavior of Cauchy problem with great data. In this report, we mainly consider the asymptotic behavior of (1.1)展开更多
Suppose that the two eigenvalues of system （0.1） are λ<sub>1</sub>（u, v）, λ<sub>2</sub>（u, v）, the corres-ponding Riemann invariants are w=w（u, v）, z=z（u, v）, and w=w（u, v）, z=z（...Suppose that the two eigenvalues of system （0.1） are λ<sub>1</sub>（u, v）, λ<sub>2</sub>（u, v）, the corres-ponding Riemann invariants are w=w（u, v）, z=z（u, v）, and w=w（u, v）, z=z（u, v） give a bijective smooth mapping from （u, v） plane onto （w, z） plane. Throughout this note, we always suppose that A<sub>1</sub> u<sub>0</sub>（x）, v<sub>0</sub>（x） are bounded measurable functions. A<sub>2</sub> λ<sub>1</sub>（u, v）, λ<sub>2</sub>（u, v）∈C<sup>1</sup> and system （0.1） are strictly hyperbolic, i.e. λ<sub>1</sub>（u, v）【λ<sub>2</sub>（u, v）.展开更多
In this note, we study the partial regularity for the weak solutions of the elliptic systems:D<sub>α</sub>(A<sub>αβ</sub><sup>ij</sup>（x,u）D<sub>β</sub>u<sup>...In this note, we study the partial regularity for the weak solutions of the elliptic systems:D<sub>α</sub>(A<sub>αβ</sub><sup>ij</sup>（x,u）D<sub>β</sub>u<sup>j</sup>)=f<sub>i</sub>（x,u,Du）, x∈Ω,i=1,2,…,N, （1）where Ω is a bounded domain in R<sup>n</sup>, n≥3 and N≥1. Here, the repeated Latin letters andrepeated Greek letters are summed from 1 to N and 1 to n respectively. We assume thefollowing conditions:展开更多
It is well known that the main characterization of BMO functions, shown by John and Nirenberg, is that their distribution function possesses an exponential decay effect. In 1980, for a bounded subset of the Nevanlinna...It is well known that the main characterization of BMO functions, shown by John and Nirenberg, is that their distribution function possesses an exponential decay effect. In 1980, for a bounded subset of the Nevanlinna class in the unit disk, Baernstein proved that the distribution function of the non-tangential maximal function decreases in an exponential way.展开更多
Complementary variational principles may be traced back to the acoustic study of Rayleigh and the study of structural mechanics of Trefftz.Since then because of their wide application, the complementary variational pr...Complementary variational principles may be traced back to the acoustic study of Rayleigh and the study of structural mechanics of Trefftz.Since then because of their wide application, the complementary variational principles have been developed rapidly.The abstract models of functional saddle theorems can be unified in an important maximum-minimum theorem, Von Neumann Theorem.展开更多
Many problems of mathematical physics especially those of partial differential equation, programming and optimal control can be solved by transforming them into variational inequalities.
文摘This paper extends symbolic dynamics to general cases. Some chaotic properties and applications of the general symbolic dynamics (Σ(X), σ) and its special cases are discussed, where X is a separable metric space.
文摘Many important results have been got in the study of application of the com pactness theory in partial differential equations. But as far as we know, there are mainly two application ways: One is the analysis of Tartar or the static structure of the Young measure; another is the analysis of Diperna of the
文摘the existence behavior of solution has been considered in many papers. Unfortunately there are no results to the asymptotic behavior of Cauchy problem with great data. In this report, we mainly consider the asymptotic behavior of (1.1)
基金Project supported by the National Natural Science Foundation of China.
文摘Suppose that the two eigenvalues of system （0.1） are λ<sub>1</sub>（u, v）, λ<sub>2</sub>（u, v）, the corres-ponding Riemann invariants are w=w（u, v）, z=z（u, v）, and w=w（u, v）, z=z（u, v） give a bijective smooth mapping from （u, v） plane onto （w, z） plane. Throughout this note, we always suppose that A<sub>1</sub> u<sub>0</sub>（x）, v<sub>0</sub>（x） are bounded measurable functions. A<sub>2</sub> λ<sub>1</sub>（u, v）, λ<sub>2</sub>（u, v）∈C<sup>1</sup> and system （0.1） are strictly hyperbolic, i.e. λ<sub>1</sub>（u, v）【λ<sub>2</sub>（u, v）.
文摘In this note, we study the partial regularity for the weak solutions of the elliptic systems:D<sub>α</sub>(A<sub>αβ</sub><sup>ij</sup>（x,u）D<sub>β</sub>u<sup>j</sup>)=f<sub>i</sub>（x,u,Du）, x∈Ω,i=1,2,…,N, （1）where Ω is a bounded domain in R<sup>n</sup>, n≥3 and N≥1. Here, the repeated Latin letters andrepeated Greek letters are summed from 1 to N and 1 to n respectively. We assume thefollowing conditions:
文摘It is well known that the main characterization of BMO functions, shown by John and Nirenberg, is that their distribution function possesses an exponential decay effect. In 1980, for a bounded subset of the Nevanlinna class in the unit disk, Baernstein proved that the distribution function of the non-tangential maximal function decreases in an exponential way.
文摘Complementary variational principles may be traced back to the acoustic study of Rayleigh and the study of structural mechanics of Trefftz.Since then because of their wide application, the complementary variational principles have been developed rapidly.The abstract models of functional saddle theorems can be unified in an important maximum-minimum theorem, Von Neumann Theorem.
文摘Many problems of mathematical physics especially those of partial differential equation, programming and optimal control can be solved by transforming them into variational inequalities.
