In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semi...In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global展开更多
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
First we introduce two necessary and sufficient conditions which ensure the existence of the global attractors for semigroup. Then we recall the concept of measure of noncompactness of a set and recapitulate its basic...First we introduce two necessary and sufficient conditions which ensure the existence of the global attractors for semigroup. Then we recall the concept of measure of noncompactness of a set and recapitulate its basic properties. Finally, we prove that these two conditions are equivalent directly.展开更多
In this article, an elliptic system is investigated, which involves Hardy-type potentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argu...In this article, an elliptic system is investigated, which involves Hardy-type potentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argument, the Palais-Smale sequences of related approximation problems is analyzed and the existence of infinitely many solutions to the system is established.展开更多
基金Supported by the NNSF of China(11031003,11271066)Supported by the Shanghai Education Commission(13ZZ048)
文摘In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global
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.
文摘First we introduce two necessary and sufficient conditions which ensure the existence of the global attractors for semigroup. Then we recall the concept of measure of noncompactness of a set and recapitulate its basic properties. Finally, we prove that these two conditions are equivalent directly.
基金supported by the Science Foundation of State Ethnic Affairs Commission of the People's Republic of China(12ZNZ004)
文摘In this article, an elliptic system is investigated, which involves Hardy-type potentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argument, the Palais-Smale sequences of related approximation problems is analyzed and the existence of infinitely many solutions to the system is established.
