In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The resul...In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The results in this paper have improved those previously related results.展开更多
Facing the impacts of climate change and the ecological environmental problems caused by urbanization, urban-rural resilience is a new value goal of territorial space development. Blue-green space is an interconnected...Facing the impacts of climate change and the ecological environmental problems caused by urbanization, urban-rural resilience is a new value goal of territorial space development. Blue-green space is an interconnected network system of natural and artificial green space and water bodies, which can dissolve the internal and external pressures of the system by way of mitigatory acceptance and adaptive interaction, reduce the impact of climate change and artificial construction disturbances, and provide diversified composite functions. By recognizing the connotation of the concept of blue-green space, its composite ecological functionality and its relationship with the value of urban-rural resilience, this paper constructs a conceptual framework for the integrated planning of blue-green space in urban and rural areas with “resilient objectives, resource identification, integrated configuration,differentiated regulation”. The paper proposes an integrated and coordinated multi-scale practicable approach of blue-green space planning(i.e., the construction of the blue-green corridor network, the configuration of blue-green open space, the allocation of blue-green infrastructure) and the regulation-based urban-rural transect, with the aim of improving the hydroecological performance and composite functional services in order to realize urban and rural resilience.展开更多
The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent dampin...The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b（t）〉 0 is effective, and in particular tb（t） →∞ as t →∞. The global existence of small energy data solutions for｜f（u）｜≈｜u｜^p in the supercritical case of p 〉 1＋ 2/n and p ≤n/n-2 for n ≥ 3 is proved.展开更多
文摘In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The results in this paper have improved those previously related results.
基金The National Natural Science Foundation of China(52008062,51908469)The Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100735)Tuojiang River Basin High-quality Development Research Center,A Key Research Base of Social Sciences in Sichuan Province(TJGZL2021-12).
文摘Facing the impacts of climate change and the ecological environmental problems caused by urbanization, urban-rural resilience is a new value goal of territorial space development. Blue-green space is an interconnected network system of natural and artificial green space and water bodies, which can dissolve the internal and external pressures of the system by way of mitigatory acceptance and adaptive interaction, reduce the impact of climate change and artificial construction disturbances, and provide diversified composite functions. By recognizing the connotation of the concept of blue-green space, its composite ecological functionality and its relationship with the value of urban-rural resilience, this paper constructs a conceptual framework for the integrated planning of blue-green space in urban and rural areas with “resilient objectives, resource identification, integrated configuration,differentiated regulation”. The paper proposes an integrated and coordinated multi-scale practicable approach of blue-green space planning(i.e., the construction of the blue-green corridor network, the configuration of blue-green open space, the allocation of blue-green infrastructure) and the regulation-based urban-rural transect, with the aim of improving the hydroecological performance and composite functional services in order to realize urban and rural resilience.
基金Project supported by a grant of DFG (Deutsche Forschungsgemeinschaft) for the research project "Influence of time-dependent coefficients on semi-linear wave models" (No. RE 961/17-1)
文摘The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b（t）〉 0 is effective, and in particular tb（t） →∞ as t →∞. The global existence of small energy data solutions for｜f（u）｜≈｜u｜^p in the supercritical case of p 〉 1＋ 2/n and p ≤n/n-2 for n ≥ 3 is proved.
