In this paper,we study the global existence of BV solutions of the initial value problem for the isentropic p-system,where the state equation of the gas is given by P=Av^(-γ).Forγ>1,the general existence result f...In this paper,we study the global existence of BV solutions of the initial value problem for the isentropic p-system,where the state equation of the gas is given by P=Av^(-γ).Forγ>1,the general existence result for large initial data has not been obtained.By using the Glimm scheme,Nishida,Smoller and Diperna successively obtained the global existence results for(γ-1)TV(v_(0)(x),u_(0)(x))being small.In the present paper,by adopting a rescaling technique,we improve these results and obtain the global existence result under the condition that(γ-1)^(γ+1)(TV(v_(0)(x)))~(γ-1)(TV(u_(0)(x)))^(2) is small,which implies that,for fixedγ>1,either TV(v_(0)(x))or TV(u_(0)(x))can be arbitrarily large.展开更多
An initial-boundary values problem in the half space （0, ∞ ） for p-system with artificial viscosity is investigated. It is shown that there exists a boundary layer solution. It is further proved that the boundary l...An initial-boundary values problem in the half space （0, ∞ ） for p-system with artificial viscosity is investigated. It is shown that there exists a boundary layer solution. It is further proved that the boundary layer solution is nonlinear stable with arbitrarily large perturbation. The proof is given by an elementary energy method.展开更多
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
In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to t...In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1 < P* less-than-or-equal-to P* < 5/4, or P* = P* = 5/4, or 5 < P* less-than-or-equal-to P* < 3/2 where P*-inf/v P and P* = sup/v P for all v under consideration, if at least one of the initial centered rarefaction waves is sufficiently strong, then the solution must be breakdown in a finite time.展开更多
We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas, the so-called p-system with viscosity. When the solution of the inviscid problem is a rar...We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas, the so-called p-system with viscosity. When the solution of the inviscid problem is a rarefaction wave with finite strength, there exists unique solution to the viscous problem with the same initial data which converges to the given inviscid solution as c goes to zero. The proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure.展开更多
The paper concerns the formation and construction of shocks. The process of transform from a smooth solution to a shock is precisely described. Meanwhile, the singularity structure and estimates of solutions near the ...The paper concerns the formation and construction of shocks. The process of transform from a smooth solution to a shock is precisely described. Meanwhile, the singularity structure and estimates of solutions near the starting point of the shock are also obtained.展开更多
We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase transition.The refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase ...We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase transition.The refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase interface.We apply the characteristic method and hodograph transform of Riemann to reduce the nonlinear PDEs to a concise form.Specially for the case of incident rarefaction wave,reduced linear equations are convenient to solve by Laplace transform.Then an integral formula in wave interaction region is derived in this paper,instead of the hypergeometric functions solutions for non-isothermal polytropic gases.It is also observed that when incident waves travel from the vapor phase to the liquid phase,the refracted waves must be accelerated and move forward.展开更多
基金partially the NSFC(11671193)Fangqi Chen was partially the NSFC(12172166,11872201)。
文摘In this paper,we study the global existence of BV solutions of the initial value problem for the isentropic p-system,where the state equation of the gas is given by P=Av^(-γ).Forγ>1,the general existence result for large initial data has not been obtained.By using the Glimm scheme,Nishida,Smoller and Diperna successively obtained the global existence results for(γ-1)TV(v_(0)(x),u_(0)(x))being small.In the present paper,by adopting a rescaling technique,we improve these results and obtain the global existence result under the condition that(γ-1)^(γ+1)(TV(v_(0)(x)))~(γ-1)(TV(u_(0)(x)))^(2) is small,which implies that,for fixedγ>1,either TV(v_(0)(x))or TV(u_(0)(x))can be arbitrarily large.
基金Partially supported by NSFC-NSAF (10676037) and NUST
文摘An initial-boundary values problem in the half space （0, ∞ ） for p-system with artificial viscosity is investigated. It is shown that there exists a boundary layer solution. It is further proved that the boundary layer solution is nonlinear stable with arbitrarily large perturbation. The proof is given by an elementary energy method.
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This work is supported in part by National Natural Science Foundation.
文摘In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1 < P* less-than-or-equal-to P* < 5/4, or P* = P* = 5/4, or 5 < P* less-than-or-equal-to P* < 3/2 where P*-inf/v P and P* = sup/v P for all v under consideration, if at least one of the initial centered rarefaction waves is sufficiently strong, then the solution must be breakdown in a finite time.
文摘We study the zero-dissipation problem for a one-dimensional model system for the isentropic flow of a compressible viscous gas, the so-called p-system with viscosity. When the solution of the inviscid problem is a rarefaction wave with finite strength, there exists unique solution to the viscous problem with the same initial data which converges to the given inviscid solution as c goes to zero. The proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure.
基金the National Natural Science Foundation of China (Grant No. 19531080) the Doctoral Program Foundation of the Ministry of Education of China.
文摘The paper concerns the formation and construction of shocks. The process of transform from a smooth solution to a shock is precisely described. Meanwhile, the singularity structure and estimates of solutions near the starting point of the shock are also obtained.
基金Supported by the National Natural Science Foundation of China(No.11901475)China Postdoctoral Science Foundation(No.2019M653815XB)Chongqing Special Postdoctoral Science Foundation(No.XmT2018045)。
文摘We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase transition.The refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase interface.We apply the characteristic method and hodograph transform of Riemann to reduce the nonlinear PDEs to a concise form.Specially for the case of incident rarefaction wave,reduced linear equations are convenient to solve by Laplace transform.Then an integral formula in wave interaction region is derived in this paper,instead of the hypergeometric functions solutions for non-isothermal polytropic gases.It is also observed that when incident waves travel from the vapor phase to the liquid phase,the refracted waves must be accelerated and move forward.
