The author extends the results in [5] to the general p(v). For arbitrary large initial data, the global smooth solution of the initial value problem is proved to be uniformly (namely, independent of time t) away from ...The author extends the results in [5] to the general p(v). For arbitrary large initial data, the global smooth solution of the initial value problem is proved to be uniformly (namely, independent of time t) away from vacuum provided that the initial data are away from vacuum.展开更多
This article considers Cauchy problem u(t) - (uv)(x) = 0, v(t) - u(x) = 0, u(x, 0) = u(0) (x) > 0, v(x, 0) = v(0)(x). A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C-1-sol...This article considers Cauchy problem u(t) - (uv)(x) = 0, v(t) - u(x) = 0, u(x, 0) = u(0) (x) > 0, v(x, 0) = v(0)(x). A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C-1-solution on t greater than or equal to 0 is obtained.展开更多
In this article, first, the authors prove that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws systems with relaxation; second, in the large time station, they p...In this article, first, the authors prove that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws systems with relaxation; second, in the large time station, they prove that the global smooth solutions of the hyperbolic conservation laws systems with relaxation converge to rarefaction waves solution at a determined L^P(p ≥ 2) decay rate.展开更多
This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 i...This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.展开更多
文摘The author extends the results in [5] to the general p(v). For arbitrary large initial data, the global smooth solution of the initial value problem is proved to be uniformly (namely, independent of time t) away from vacuum provided that the initial data are away from vacuum.
基金Project supported by the NSF of Fujian Province (A97020)
文摘This article considers Cauchy problem u(t) - (uv)(x) = 0, v(t) - u(x) = 0, u(x, 0) = u(0) (x) > 0, v(x, 0) = v(0)(x). A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C-1-solution on t greater than or equal to 0 is obtained.
基金This research is supported by "Foundation of office of overseas Chinese affair under the state council: 03QZR09"
文摘In this article, first, the authors prove that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws systems with relaxation; second, in the large time station, they prove that the global smooth solutions of the hyperbolic conservation laws systems with relaxation converge to rarefaction waves solution at a determined L^P(p ≥ 2) decay rate.
基金Project supported by the NSF of China! (19971O62)the NSF of Fujian Province!(A97020) the NSF of Educational Committee of
文摘This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.