In this paper, we investigate the basic properties of C-cosine family and characterize the densely defined generator of exponential bounded C-cosine family by making use of the theory of vector value Laplace transform...In this paper, we investigate the basic properties of C-cosine family and characterize the densely defined generator of exponential bounded C-cosine family by making use of the theory of vector value Laplace transform. Moreover, we apply this theory to the second order Cauchy problem.展开更多
基金国家自然科学基金(批准号:61403313,61374078)重庆市基础与前沿研究计划重点项目(批准号:cstc2015jcyj BX0052)+2 种基金重庆市基础与前沿研究计划一般项目(批准号:cstc2014jcyj A40014)中央高校基本科研业务费(批准号:XDJK2016B017,XDJK2016E032)Qatar National Research Fund(Grant No.NPRP 7-1482-1-278)资助项目
文摘In this paper, we investigate the basic properties of C-cosine family and characterize the densely defined generator of exponential bounded C-cosine family by making use of the theory of vector value Laplace transform. Moreover, we apply this theory to the second order Cauchy problem.