In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for ...In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.展开更多
In this paper, we study the global existence of weak solutions for the Cauchy problem of the nonlinear hyperbolic system of three equations(1.1) with bounded initial data(1.2). When we fix the third variable s, the sy...In this paper, we study the global existence of weak solutions for the Cauchy problem of the nonlinear hyperbolic system of three equations(1.1) with bounded initial data(1.2). When we fix the third variable s, the system about the variables ρ and u is the classical isentropic gas dynamics in Eulerian coordinates with the pressure function P(ρ, s) = ese-1/ρ,which, in general, does not form a bounded invariant region. We introduce a variant of the viscosity argument, and construct the approximate solutions of(1.1) and(1.2) by adding the artificial viscosity to the Riemann invariants system(2.1). When the amplitude of the first two Riemann invariants(w1(x, 0), w2(x, 0)) of system(1.1) is small,(w1(x, 0), w2(x, 0)) are nondecreasing and the third Riemann invariant s(x, 0) is of the bounded total variation, we obtained the necessary estimates and the pointwise convergence of the viscosity solutions by the compensated compactness theory. This is an extension of the results in [1].展开更多
In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and...In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and prove that the global weak solutions of each system could be obtained by the limit of the linear combination of two systems.展开更多
In this paper, we construct a sequence of hyperbolic systems (13) to approximate the general system of one-dimensional nonlinear elasticity in Lagrangian coordinates (2). For each fixed approximation parameter , we es...In this paper, we construct a sequence of hyperbolic systems (13) to approximate the general system of one-dimensional nonlinear elasticity in Lagrangian coordinates (2). For each fixed approximation parameter , we establish the existence of entropy solutions for the Cauchy problem (13) with bounded initial data (23).展开更多
基金supported by the Zhejiang Natural Science Foundation of China(LQ13A010022)supported by the Qianjiang professorship of Zhejiang Province of Chinathe National Natural Science Foundation of China(11271105)
文摘In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.
基金supported by the the NSFC(LY20A010023)a professorship called Qianjiang scholar of Zhejiang Province of China.
文摘In this paper, we study the global existence of weak solutions for the Cauchy problem of the nonlinear hyperbolic system of three equations(1.1) with bounded initial data(1.2). When we fix the third variable s, the system about the variables ρ and u is the classical isentropic gas dynamics in Eulerian coordinates with the pressure function P(ρ, s) = ese-1/ρ,which, in general, does not form a bounded invariant region. We introduce a variant of the viscosity argument, and construct the approximate solutions of(1.1) and(1.2) by adding the artificial viscosity to the Riemann invariants system(2.1). When the amplitude of the first two Riemann invariants(w1(x, 0), w2(x, 0)) of system(1.1) is small,(w1(x, 0), w2(x, 0)) are nondecreasing and the third Riemann invariant s(x, 0) is of the bounded total variation, we obtained the necessary estimates and the pointwise convergence of the viscosity solutions by the compensated compactness theory. This is an extension of the results in [1].
文摘In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and prove that the global weak solutions of each system could be obtained by the limit of the linear combination of two systems.
文摘In this paper, we construct a sequence of hyperbolic systems (13) to approximate the general system of one-dimensional nonlinear elasticity in Lagrangian coordinates (2). For each fixed approximation parameter , we establish the existence of entropy solutions for the Cauchy problem (13) with bounded initial data (23).
