This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solu...This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.展开更多
This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotrop...This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.展开更多
In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditi...In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.展开更多
In this paper the following nonlinear degenerate parabolic systemsu t=Δ x( grad φ(u))+α·Δb(u)+f(x,t,u)with Dirichlet boundary conditions are discussed, where u, grad φ(u),b and f are vector value...In this paper the following nonlinear degenerate parabolic systemsu t=Δ x( grad φ(u))+α·Δb(u)+f(x,t,u)with Dirichlet boundary conditions are discussed, where u, grad φ(u),b and f are vector valued functions and x∈Ω R N. Under some structure conditions on the terms of the systems, the results on existence and uniqueness of global solutions of the systems are established.展开更多
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of so...This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vázquez and the comparison principle, we deduce that the blow-up occurs only on the boundary ?Ω. In addition, for a bounded Lipschitz domain Ω, we establish the blow-up rate estimates for the positive solution to this problem with a = 0.展开更多
Objective： To observe the effect of hydroxysafflor yellow A （HSYA）, an active ingredient of a traditional Chinese herbal medicine Carthamus tinctorius L., on lung inflammation and pulmonary fibrosis induced by bleo...Objective： To observe the effect of hydroxysafflor yellow A （HSYA）, an active ingredient of a traditional Chinese herbal medicine Carthamus tinctorius L., on lung inflammation and pulmonary fibrosis induced by bleomycin （BLM） in rats. Methods： Animals were divided into 6 groups including normal group, model group, three HSYA groups and dexamethasone （DXM） group. Three doses of HSYA （35.6, 53.3, and 80.0 mg？kg–1？day–1） were intraperitoneally （i.p.） injected in rats for 3 weeks after BLM administration and DXM was used as the positive control （n=8 or 12）. Arterial blood gas was assayed and morphological changes were observed. Lung mRNA expressions of tumor necrosis factor （TNF）-α, interleukin （IL）-1β, IL-6 and some cytokines in lung tissue were detected by real-time polymerase chain reaction. Nuclear factor-κB p65 or α-smooth muscle actin （α-SMA） protein distribution in rat lung tissue was observed by immunohistochemistry. Results： On the 7th day after BLM administration, lung tissue showed serious inflammation. Treatment with HSYA or DXM ameliorated lung inflammation. After treatment with HSYA or DXM, oxygen partial pressure （PaO2） increased （HSYA 80.0 mg？kg–1, P〈0.01） and CO2 partial pressure （PaCO2） decreased （HSYA 53.3, 80.0 mg？kg–1, P〈0.05）. Moreover, the mRNA expression of TNF-α, IL-1β, and IL-6; and the number of NF-κB p65 positive cells was lower in HSYA 53.3 and 80.0 mg？kg–1 groups than those in the model group （all P〈0.05）. Twenty-one days after BLM administration, HSYA or DXM treatment ameliorated fibrosis, increased PaO2 （HSYA 53.3, 80.0 mg？kg–1, P〈0.01）, and decreased PaCO2 （53.3 and 80.0 mg？kg–1, P〈0.05）. Further, the mRNA expression of TGF-β1, α-SMA, and collagen Ⅰ as well as the number of α-SMA positive cells increased in the model group and HSYA can attenuate these changes （53.3, 80.0 mg？kg–1, P〈0.05）. Hematoxylin and eosin and Masson＇s trichrome staining indicated th展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant Nos.10471013,10471022)the Ministry of Education of China Science and Technology Major Projects (Grant No.104090)
文摘This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.
基金The project is supported by NNSF of China (10371116)
文摘This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.
基金the National Natural Science Foundation of China (Grant No. 10531020)
文摘In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.
文摘In this paper the following nonlinear degenerate parabolic systemsu t=Δ x( grad φ(u))+α·Δb(u)+f(x,t,u)with Dirichlet boundary conditions are discussed, where u, grad φ(u),b and f are vector valued functions and x∈Ω R N. Under some structure conditions on the terms of the systems, the results on existence and uniqueness of global solutions of the systems are established.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471022 and 10601011)Key Project of the Ministry of Education of China (Grant No. 104090)
文摘This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vázquez and the comparison principle, we deduce that the blow-up occurs only on the boundary ?Ω. In addition, for a bounded Lipschitz domain Ω, we establish the blow-up rate estimates for the positive solution to this problem with a = 0.
基金Supported by Traditional Chinese Medicine Development Foundation of Beijing(No.JJ-2009-22)Natural Science Foundation of Beijing(No.7132047)
文摘Objective： To observe the effect of hydroxysafflor yellow A （HSYA）, an active ingredient of a traditional Chinese herbal medicine Carthamus tinctorius L., on lung inflammation and pulmonary fibrosis induced by bleomycin （BLM） in rats. Methods： Animals were divided into 6 groups including normal group, model group, three HSYA groups and dexamethasone （DXM） group. Three doses of HSYA （35.6, 53.3, and 80.0 mg？kg–1？day–1） were intraperitoneally （i.p.） injected in rats for 3 weeks after BLM administration and DXM was used as the positive control （n=8 or 12）. Arterial blood gas was assayed and morphological changes were observed. Lung mRNA expressions of tumor necrosis factor （TNF）-α, interleukin （IL）-1β, IL-6 and some cytokines in lung tissue were detected by real-time polymerase chain reaction. Nuclear factor-κB p65 or α-smooth muscle actin （α-SMA） protein distribution in rat lung tissue was observed by immunohistochemistry. Results： On the 7th day after BLM administration, lung tissue showed serious inflammation. Treatment with HSYA or DXM ameliorated lung inflammation. After treatment with HSYA or DXM, oxygen partial pressure （PaO2） increased （HSYA 80.0 mg？kg–1, P〈0.01） and CO2 partial pressure （PaCO2） decreased （HSYA 53.3, 80.0 mg？kg–1, P〈0.05）. Moreover, the mRNA expression of TNF-α, IL-1β, and IL-6; and the number of NF-κB p65 positive cells was lower in HSYA 53.3 and 80.0 mg？kg–1 groups than those in the model group （all P〈0.05）. Twenty-one days after BLM administration, HSYA or DXM treatment ameliorated fibrosis, increased PaO2 （HSYA 53.3, 80.0 mg？kg–1, P〈0.01）, and decreased PaCO2 （53.3 and 80.0 mg？kg–1, P〈0.05）. Further, the mRNA expression of TGF-β1, α-SMA, and collagen Ⅰ as well as the number of α-SMA positive cells increased in the model group and HSYA can attenuate these changes （53.3, 80.0 mg？kg–1, P〈0.05）. Hematoxylin and eosin and Masson＇s trichrome staining indicated th
