In this paper,we propose a second-order quasilinear hyperbolic system.By means of the theory on semi-global C^(1)solution to first-order quasilinear hyperbolic systems,we establish the existence and uniqueness of semi...In this paper,we propose a second-order quasilinear hyperbolic system.By means of the theory on semi-global C^(1)solution to first-order quasilinear hyperbolic systems,we establish the existence and uniqueness of semi-global C^(2)solution to this second-order quasilinear hyperbolic system.After then,the general constructive framework is utilized to obtain the local exact boundary controllability for this second-order system.展开更多
In this paper,we first survey existed theorems and propose all 46 related open problems of the existence of global attractors for autonomous dynamical systems,then establish a new existence theorem of global attractor...In this paper,we first survey existed theorems and propose all 46 related open problems of the existence of global attractors for autonomous dynamical systems,then establish a new existence theorem of global attractors which will be applied to a nonclassical diffusion equation for the norm-to-weak continuous,weakly compact semigroup on H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively.As an application of this new existence theorem of global attractors,we obtain the existence of the global attractors on H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively for a nonclassical-diffusion equation.展开更多
We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation.What is more,each soliton molecule can be transformed into an asymmetr...We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation.What is more,each soliton molecule can be transformed into an asymmetric soliton by changing the parameterφ.In addition,the collision between soliton molecules(or asymmetric soliton)and several soliton solutions is observed.Finally,some related pictures are presented.展开更多
Soliton molecules have become one of the hot topics in recent years. In this article, we investigate soliton molecules and some novel hybrid solutions for the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kau...Soliton molecules have become one of the hot topics in recent years. In this article, we investigate soliton molecules and some novel hybrid solutions for the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt(gKDKK) equation by using the velocity resonance, module resonance, and long wave limits methods. By selecting some specific parameters, we can obtain soliton molecules and asymmetric soliton molecules of the gKDKK equation. And the interactions among N-soliton molecules are elastic. Furthermore, some novel hybrid solutions of the gKDKK equation can be obtained, which are composed of lumps,breathers, soliton molecules and asymmetric soliton molecules. Finally, the images of soliton molecules and some novel hybrid solutions are given, and their dynamic behavior is analyzed.展开更多
For the Cauchy problem to Keller–Segel system,we show well-posedness and time-decay estimates in the critical scaling-invariant Besov spaces by using Littlewood–Paley analysis together with the decay estimates of he...For the Cauchy problem to Keller–Segel system,we show well-posedness and time-decay estimates in the critical scaling-invariant Besov spaces by using Littlewood–Paley analysis together with the decay estimates of heat kernels.展开更多
The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the gener...The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the general M-lump,high-order breather,and localized interaction hybrid solutions are investigated,respectively.Then we implement the numerical simulations to research their dynamical behaviors,which indicate that different parameters have very different dynamic properties and propagation modes of the waves.The method involved can be validly employed to get high-order waves and study their propagation phenomena of many nonlinear equations.展开更多
基金Supported by the Science and Technology Commission of Shanghai Municipality (Grant No.23ZR1402100)the Fundamental Research Funds for the Central Universities (Grant Nos. 2232022G-13 and 2232023G-13)
文摘In this paper,we propose a second-order quasilinear hyperbolic system.By means of the theory on semi-global C^(1)solution to first-order quasilinear hyperbolic systems,we establish the existence and uniqueness of semi-global C^(2)solution to this second-order quasilinear hyperbolic system.After then,the general constructive framework is utilized to obtain the local exact boundary controllability for this second-order system.
基金Supported by the NNSF of China(Grant No.12171082)The fundamental research funds for the central universities(Grant Nos.2232022G-13 and 2232023G-13)by a grant from Science and Technology Commission of Shanghai Municipality。
文摘In this paper,we first survey existed theorems and propose all 46 related open problems of the existence of global attractors for autonomous dynamical systems,then establish a new existence theorem of global attractors which will be applied to a nonclassical diffusion equation for the norm-to-weak continuous,weakly compact semigroup on H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively.As an application of this new existence theorem of global attractors,we obtain the existence of the global attractors on H_(0)^(1)(Ω)and H^(2)(Ω)∩H_(0)^(1)(Ω)respectively for a nonclassical-diffusion equation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11371086, 11671258, and 11975145)the Fund of Science and Technology Commission of Shanghai Municipality, China (Grant No. 13ZR1400100)+1 种基金the Fund of Institute for Nonlinear Sciences, Donghua Universitythe Fundamental Research Funds for the Central Universities, China (Grant No. 2232021G-13)
文摘We investigate the techniques for velocity resonance and apply them to construct soliton molecules using two solitons of the extended Lax equation.What is more,each soliton molecule can be transformed into an asymmetric soliton by changing the parameterφ.In addition,the collision between soliton molecules(or asymmetric soliton)and several soliton solutions is observed.Finally,some related pictures are presented.
基金supported by the National Natural Science Foundation of China (project Nos. 11371086,11671258,11975145)the Fund of Science and Technology Commission of Shanghai Municipality (project No. 13ZR1400100)the Fund of Donghua University,Institute for Nonlinear Sciences and the Fundamental Research Funds for the Central Universities。
文摘Soliton molecules have become one of the hot topics in recent years. In this article, we investigate soliton molecules and some novel hybrid solutions for the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt(gKDKK) equation by using the velocity resonance, module resonance, and long wave limits methods. By selecting some specific parameters, we can obtain soliton molecules and asymmetric soliton molecules of the gKDKK equation. And the interactions among N-soliton molecules are elastic. Furthermore, some novel hybrid solutions of the gKDKK equation can be obtained, which are composed of lumps,breathers, soliton molecules and asymmetric soliton molecules. Finally, the images of soliton molecules and some novel hybrid solutions are given, and their dynamic behavior is analyzed.
文摘For the Cauchy problem to Keller–Segel system,we show well-posedness and time-decay estimates in the critical scaling-invariant Besov spaces by using Littlewood–Paley analysis together with the decay estimates of heat kernels.
基金The work was supported by the National Natural Science Foundation of China(Grant Nos.11371086,11671258,11975145)the Fund of Science and Technology Commission of Shanghai Municipality(No.13ZR1400100)the Fund of Donghua University,Institute for Nonlinear Sciences,and the Fundamental Research Funds for the Central Universitieswith contract number 2232021G-13.
文摘The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the general M-lump,high-order breather,and localized interaction hybrid solutions are investigated,respectively.Then we implement the numerical simulations to research their dynamical behaviors,which indicate that different parameters have very different dynamic properties and propagation modes of the waves.The method involved can be validly employed to get high-order waves and study their propagation phenomena of many nonlinear equations.
