We study a semilinear parabolic problem with a semilinear dynamical boundary condition in an irregular domain with fractal boundary. Local existence, uniqueness and regularity results for the mild solution, are establ...We study a semilinear parabolic problem with a semilinear dynamical boundary condition in an irregular domain with fractal boundary. Local existence, uniqueness and regularity results for the mild solution, are established via a semigroup approach. A sufficient condition on the initial datum for global existence is given.展开更多
Most systems arising in engineering fields are spatiotemporal processes in nature so that their behavior must depend on time as well as spatial position.These spatiotemporal processes are in general modeled by partial...Most systems arising in engineering fields are spatiotemporal processes in nature so that their behavior must depend on time as well as spatial position.These spatiotemporal processes are in general modeled by partial differential equations.Substantial literature on the research of distributed parameter systems(DPSs)has been reported over the past decades.Amount of results on analysis and control of DPSs have been developed in these research articles,which include not only extensions of finite-dimensional techniques to infinite-dimensional systems but also innovative infinite-dimensional analysis and control design approaches.Hence,a comprehensive survey of all the developments of DPSs is perhaps a very difficult task.This paper,however,attempts to present a brief yet reasonable overview of research on the analysis and control of distributed parameter systems for applications.To help readers,some simple mathematical descriptions and necessary figures are involved in this article.Finally,some open areas of research and possible directions have also been outlined.展开更多
文摘We study a semilinear parabolic problem with a semilinear dynamical boundary condition in an irregular domain with fractal boundary. Local existence, uniqueness and regularity results for the mild solution, are established via a semigroup approach. A sufficient condition on the initial datum for global existence is given.
基金This project is supported by the Natural Science Foundation of China and the Science Founda-tion of Science and Technology Committee of Shanghai(N.OOJC140 5 7)
基金supported by the National Science Fund for Distinguished Young Scholars(61125306)the National Natural Science Foundation of China(6107405791016004)
文摘Most systems arising in engineering fields are spatiotemporal processes in nature so that their behavior must depend on time as well as spatial position.These spatiotemporal processes are in general modeled by partial differential equations.Substantial literature on the research of distributed parameter systems(DPSs)has been reported over the past decades.Amount of results on analysis and control of DPSs have been developed in these research articles,which include not only extensions of finite-dimensional techniques to infinite-dimensional systems but also innovative infinite-dimensional analysis and control design approaches.Hence,a comprehensive survey of all the developments of DPSs is perhaps a very difficult task.This paper,however,attempts to present a brief yet reasonable overview of research on the analysis and control of distributed parameter systems for applications.To help readers,some simple mathematical descriptions and necessary figures are involved in this article.Finally,some open areas of research and possible directions have also been outlined.
