In this paper a Verigin problem with kinetic condition is considered. The existence and uniqueness of a classical solution locally in time of this problem are obtained.
In this paper,we consider a kind of quasilinear hyperbolic systems with inhomogeneous terms satisfying dissipative condition or matching condition.For the Cauchy problem of this kind of systems,we prove that,if the in...In this paper,we consider a kind of quasilinear hyperbolic systems with inhomogeneous terms satisfying dissipative condition or matching condition.For the Cauchy problem of this kind of systems,we prove that,if the initial data is small and satisfies some decay condition,and the system is weakly linearly degenerate,then the Cauchy problem admits a unique global classical solution on t ≥ 0.展开更多
The author considers Verigin problem with surface tension.Under natural conditions the existence of classical solution locally in time is proved by Schauder fixed point theorem.
In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost （resp. leftmost） eigenvalue is w...In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost （resp. leftmost） eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C^1 solution with small and decaying initial data.展开更多
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 th...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.展开更多
文摘In this paper a Verigin problem with kinetic condition is considered. The existence and uniqueness of a classical solution locally in time of this problem are obtained.
基金Supported by National Science Foundation of China（10671124）
文摘In this paper,we consider a kind of quasilinear hyperbolic systems with inhomogeneous terms satisfying dissipative condition or matching condition.For the Cauchy problem of this kind of systems,we prove that,if the initial data is small and satisfies some decay condition,and the system is weakly linearly degenerate,then the Cauchy problem admits a unique global classical solution on t ≥ 0.
文摘The author considers Verigin problem with surface tension.Under natural conditions the existence of classical solution locally in time is proved by Schauder fixed point theorem.
文摘In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost （resp. leftmost） eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C^1 solution with small and decaying initial data.
基金Supported by the National Natural Science Foundation of China (Grant No.10771038)
文摘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.
