GLOBAL EXISTENCE OF THE SOLUTIONS OF NONLINEAR PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

This paper deals with the following IBV problem of nonlinear parabolic equation: where Ω is the exterior domain of a compact set in R~n with smooth boundary and F satisfies |F(λ)|=o(|λ|~2), near λ=0. It is proved that when n≥3, under the suitable smoothness and compatibility conditions, the above problem has a unique global smooth solution for small initial data. Moreover, It is also proved that the solution has the decay property ‖u(t)‖_(L∞(Ω)=o(t~(-n/2)), as t→ ∞.     

GLOBAL EXISTENCE OF THE SOLUTIONS TO NONLINEAR HYPERBOLIC EQUATIONS IN EXTERIOR DOMAINS

This paper deals with the following IBV problem of nonlinear hyperbolic equations u_(tt)- sum from i, j=1 to n a_(jj)(u, Du)u_(x_ix_j)=b(u, Du), t>0, x∈Ω, u(O, x) =u~0(x), u_t(O, x) =u~1(v), x∈Ω, u(t, x)=O t>O, x∈()Ω,where Ωis the exterior domain of a compact set in R~n, and |a_(ij)(y)-δ_(ij)|= O(|y|~k), |b(y)|=O(|y|~(k+1)), near y=O. It is proved that under suitable assumptions on the smoothness,compatibility conditions and the shape of Ω, the above problem has a unique global smoothsolution for small initial data, in the case that k=1 add n≥7 or that k=2 and n≥4.Moreover, the solution ham some decay properties as t→ + ∞.     

ON THE HYPER-ORDER OF MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

In this paper the order and the hyper-order of the solutions of higher-order homoge-neous linear differential equations is investigated.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE SYSTEM OF ONE-DIMENSIONAL NONLINEAR THERMOVISCOELASTICITY

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｄｅｖｏｔｅｄｔｏｔｈｅｓｔｕｄｙｏｆｔｈｅｌａｒｇｅｔｉｍｅｂｅｈａｖｉｏｕｒｏｆｓｍｏｏｔｈｓｏｌｕｔｉｏｎｓｆｏｒｉｎｉｔｉａｌｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｉｎｏｎｅｄｉ...     

EXTENDABILITY OF SOLUTIONS FOR THE LINEAR SYSTEM OF ELLIPTIC TYPE EQUATIONS

The solutions of linear system of elliptic type equations with first order isdiscussed by using the method of several complex analysis and, a series of newextended results of the solutions for the system of elliptic type are obtained.     

ON THE EXISTENCE THEOREMS OF NONTRIVIAL PERIODIC SOLUTIONS TOA CLASS OF NONLINEAR NON－AUTONOMOUS SYS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＮＯＮＴＲＩＶＩＡＬＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＴＯＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＮＯＮ－ＡＵＴＯＮＯＭＯＵＳＳＹＳＴＥＭＳ￥ＧａｏＺｈａｎｈａｉ（高占海）；ＺｈａｎｇＤｉ（张棣）（Ｎｏｒｔｈ...     

ON THE CONTINUABILITY OF SOLUTIONS IN THE FUTURE FOR THE LIENARD SYSTEM

ＯＮＴＨＥＣＯＮＴＩＮＵＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＩＮＴＨＥＦＵＴＵＲＥＦＯＲＴＨＥＬＩＥＮＡＲＤＳＹＳＴＥＭＨｕａｎｇＬｉｈｏｎｇ（黄立宏）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，湖南大学，邮编：４１００８２）Ａｂｓｔｒａｃｔ：Ｔｈｅｍａｉｎｐ...     

ON THE NON-EXISTENCE OF PERIODIC SOLUTIONS OF A GENERALIZED LIENARD SYSTEM

ＯＮＴＨＥＮＯＮ－ＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＡ　ＧＥＮＥＲＡＬＩＺＥＤＬＩＥＮＡＲＤＳＹＳＴＥＭＨｕａｎｇＬｉｈｏｎｇ（黄立宏）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｓｏｍｅｋｎ...     

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.     

A REMARK ON THE ATTRACTORS OF NON－NEWTONIAN FLUIDS

This paper corrects some mistakes in the proof of absorbing sets theorem of attractors of non-Newtonian fluids, and establishes again the existence of bounded absorbing sets.     

ON THE BOUNDEDNESS CONDITIONS FOR SOLUTIONS OF A AUTONOMOUS DIFFERENTIAL SYSTEM

ＯＮＴＨＥＢＯＵＮＤＥＤＮＥＳＳＣＯＮＤＩＴＩＯＮＳＦＯＲＳＯＬＵＴＩＯＮＳＯＦＡＡＵＴＯＮＯＭＯＵＳＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭ￥ＨｕａｎｇＬｉｈｏｎｇ（黄立宏）；ＷａｎｇＺｈｉｃｈｅｎｇ（王志成）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，湖南大学...     

THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF INITIAL VALUE PROBLEM TO SYSTEM OF GAS DYNAMICS WITH VISCOSITY

This paper considers the system where with where provided orThe traveling wave solution of problem (A), (B) is proved to be asymptoically stable when (C)_1, (C)_2 are satisfied and rarefaction wave solution is proved to be asymptotical when (C)_3, (C)_4 are satisfied, provided that the initial disturbance is suitably small and of zero constant component. The proof is given by the elemental L~2 energy method.     

ON THE HOLOMORPHIC PROPERTY OF THE SEMIGROUP ASSOCIATED WITH LINEAR ELASTIC SYSTEMS WITH STRUCTURAL DAMPING

G. Chen and D. L. Russell studied the following linear elastic systems with structural damping     

ON THE ASYMPTOTIC ASSIGNMENT OF THE BOUNDS OF DECREASING RATE FOR A TIME-VARYING LINEAR CONTROL SYSTEM

In the paper the problem on the assignment of the bounds of decreasing rate for a time-varying linear control system is discussed. The sufficient and necessary condition for bounds of decreasing rate of a time-varying linear system to be assigned arbitrarily is presented. It is pointed out that for any given real number n, M, n相似文献   

GLOBAL BEHAVIOUR OF THE SOLUTIONS OF A CLASS OF THREE－DIMENSIONSAL COMPETITIVE SYSTEM

ＧＬＯＢＡＬＢＥＨＡＶＩＯＵＲＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦＡＣＬＡＳＳＯＦＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＳＡＬＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＣｈｅｎｇＣｈｕｎＣｈｏｒＬｉｔｗｉｎ（ＨｏｎｇＫｏｎｇＩｎｓｔｉｔｕｔｅＯｆＥｄｕｃａｔｉｏｎ）Ａｂ...     

THE NON－EXISTENCE OF PERIODIC SOLUTIONS OF A CERTAIN CLASS OF N－TH ORDER DIFFERENTIAL EQUATIONS

ＴＨＥ　ＮＯＮ－ＥＸＩＳＴＥＮＣＥ　ＯＦ　ＰＥＲＩＯＤＩＣ　ＳＯＬＵＴＩＯＮＳ　ＯＦ　Ａ　ＣＥＲＴＡＩＮ　ＣＬＡＳＳ　ＯＦ　Ｎ－ＴＨ　ＯＲＤＥＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＴＨＥＮＯＮ－ＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵ...     

A NOTE ON THE GLOBAL SOLUTIONS OF A SEMILINEAR REACTION DIFFUSION SYSTEM

ＡＮＯＴＥＯＮＴＨＥＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＯＦＡＳＥＭＩＬＩＮＥＡＲＲＥＡＣＴＩＯＮＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭ（王明新，吴永辉）￥ＷａｎｇＭｉｎｇｘｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓＭｅｃｈａｎｉｃｓ，ＳｏｕｔｈｅａｓｔＵｎｉｖ，...     

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

This paper is a continuation of the authors'previous paper[1].In this paper the authorsprove,assuming additional conditions on the initial data,some results about the existence anduniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolicsystem a_t+(au)_x_2au/x=0,u_t+1/2(a~2+u~2)_x=0,x>0,t≥0.     

NEW RESULTS ON THE EXPONENTIAL STABILITY OF NON－STATIONARY POPULATION DYNAMICS

ＮＥＷＲＥＳＵＬＴＳＯＮＴＨＥＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＴＹＯＦＮＯＮ－ＳＴＡＴＩＯＮＡＲＹＰＯＰＵＬＡＴＩＯＮＤＹＮＡＭＩＣＳ￥（郭宝珠，姚翠珍）ＧｕｏＢａｏｚｈｕ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｂｅｉｊｉ...     

LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...