In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx...In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.展开更多
This paper is concerned with the existence and uniqueness of nonnegative classical solutions to the initial-boundary value problems for the pseudo-parabolic equation with strongly nonlinear sources. Furthermore, we di...This paper is concerned with the existence and uniqueness of nonnegative classical solutions to the initial-boundary value problems for the pseudo-parabolic equation with strongly nonlinear sources. Furthermore, we discuss the asymptotic behavior of solutions as the viscosity coefficient k tends to zero.展开更多
In this paper, we prove the existence of nonnegative solutions to the initial boundary value problems for the pseudo-parabolic type equation with weakly nonlin- ear sources. Further, we discuss the asymptotic behavior...In this paper, we prove the existence of nonnegative solutions to the initial boundary value problems for the pseudo-parabolic type equation with weakly nonlin- ear sources. Further, we discuss the asymptotic behavior of the solutions as the viscous coefficient k tends to zero.展开更多
In this paper we consider the initial boundary value problem of a higher order viscous diffusion equation with gradient dependent potentials Φ（s） and sources A（s）. We first show the general existence and uniquene...In this paper we consider the initial boundary value problem of a higher order viscous diffusion equation with gradient dependent potentials Φ（s） and sources A（s）. We first show the general existence and uniqueness of global classical solutions provided that the first order derivatives of both Φ（s） and A（s） are bounded below. Such a restriction is almost necessary, namely, if one of the derivatives is unbounded from below, then the solution might blow up in a finite time. A more interesting phenomenon is also revealed for potentials or sources being unbounded from below. In fact, if either the source or the potential is dominant, then the solution will blow up definitely in a finite time. Moreover, the viscous coefficient might postpone the blow-up time. Exactly speaking, for any T 〉 0, the solution will never blow up during the period 0 〈 t 〈 T, so long as thc viscous coefficient is large enough.展开更多
基金Supported by the National Natural Science Foundation of China（10671182）
文摘In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.
基金The NSFC,CPSF,SRFDP and 973 Program(2010CB808002)
文摘This paper is concerned with the existence and uniqueness of nonnegative classical solutions to the initial-boundary value problems for the pseudo-parabolic equation with strongly nonlinear sources. Furthermore, we discuss the asymptotic behavior of solutions as the viscosity coefficient k tends to zero.
文摘In this paper, we prove the existence of nonnegative solutions to the initial boundary value problems for the pseudo-parabolic type equation with weakly nonlin- ear sources. Further, we discuss the asymptotic behavior of the solutions as the viscous coefficient k tends to zero.
基金Supported by the NSF of China(Grant Nos.11371153,11471127,11571062,11671155 and 11771156)NSF of Guangdong(Grant No.2016A030313418)+1 种基金NSF of Guangzhou(Grant Nos.201607010207 and 201707010136)the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK01)
文摘In this paper we consider the initial boundary value problem of a higher order viscous diffusion equation with gradient dependent potentials Φ（s） and sources A（s）. We first show the general existence and uniqueness of global classical solutions provided that the first order derivatives of both Φ（s） and A（s） are bounded below. Such a restriction is almost necessary, namely, if one of the derivatives is unbounded from below, then the solution might blow up in a finite time. A more interesting phenomenon is also revealed for potentials or sources being unbounded from below. In fact, if either the source or the potential is dominant, then the solution will blow up definitely in a finite time. Moreover, the viscous coefficient might postpone the blow-up time. Exactly speaking, for any T 〉 0, the solution will never blow up during the period 0 〈 t 〈 T, so long as thc viscous coefficient is large enough.
