This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ i...This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →＋∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.展开更多
We prove the two existence results of the radially symmetric strong solutions to the Navier- Stokes-Poisson equations for isentropic compressible fluids. The important point in this paper is that the initial density i...We prove the two existence results of the radially symmetric strong solutions to the Navier- Stokes-Poisson equations for isentropic compressible fluids. The important point in this paper is that the initial density is vacuum. It is different from weak solutions. Now we need some compatibility condition.展开更多
In this paper we introduce a new deformation argument,in which C^(0)-group action and a new ty pe of Palais Smale condition PSP play important roles.This type of deformation results are studied in[17,21]and has many d...In this paper we introduce a new deformation argument,in which C^(0)-group action and a new ty pe of Palais Smale condition PSP play important roles.This type of deformation results are studied in[17,21]and has many different applications[10,11,17,21]et al.Typically it can be applied to nonlinear scalar field equations.We give a survey in an abstract functional setting.We also present another application to nonlinear elliptic problems in strip-like domains.Under conditions related to[5,6],we show the existence of infinitely many solutions.This ex tends the results in[8].展开更多
基金Project supported by Grant-in-Aid for Science Research (No.12740105, No.14204011), JSPS.
文摘This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →＋∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.
基金Supported by NSF of China (No.10531020)the Program of 985 Innovation Engineering on Information in Xiamen University(2004-2007)NCETXMU
文摘We prove the two existence results of the radially symmetric strong solutions to the Navier- Stokes-Poisson equations for isentropic compressible fluids. The important point in this paper is that the initial density is vacuum. It is different from weak solutions. Now we need some compatibility condition.
基金The first author is supported by PRIN 2017JPCAPN“Qualitative and quantitative aspects of nonlinear PDEs”and by INdAM-GNAMPAThe second author is supported in part by Grant-in-Aid for Scientific Research(JP19H00644,JP18KK0073,JP17H02855,JP16K13771 and JP26247014)of Japan Society for the Promotion of Science.
文摘In this paper we introduce a new deformation argument,in which C^(0)-group action and a new ty pe of Palais Smale condition PSP play important roles.This type of deformation results are studied in[17,21]and has many different applications[10,11,17,21]et al.Typically it can be applied to nonlinear scalar field equations.We give a survey in an abstract functional setting.We also present another application to nonlinear elliptic problems in strip-like domains.Under conditions related to[5,6],we show the existence of infinitely many solutions.This ex tends the results in[8].
