This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standar...This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].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 paper, we study the following Cauchy problem.and obtain the convergence of L bounded approximating Sequences generated by the methodof vanishing viscidity and compensated compactness.
基金Huijiang Zhao was supported by the National Natural Science Foundation of China (10871151)Changjiang Zhu was supported by the National Natural Science Foundation of China (10625105 and 10431060)the Program for New Century Excellent Talentsin University (NCET-04-0745)
文摘This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].
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 paper, we study the following Cauchy problem.and obtain the convergence of L bounded approximating Sequences generated by the methodof vanishing viscidity and compensated compactness.
