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1.  THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH TIME DELAY  被引次数:7
   莫嘉琪  冯茂春《数学物理学报(B辑英文版)》,2001年第2期
   Mo studied a class of singularly perturbed problems for reaction diffusion equations in[4]-[8]. Now we consider the following nonlinear singularly perturbed prob1em with time delaywhere i = 1, 2,' l N, u = (u1, u2l', UN), u* = (u1, u;,', uX) and u: == ui(t -- er, xt e) (thereis similar notation of the superscript k*" below), rt e are positive C..,tant. and re is the timedelay, andz = (xl, xzl... l z.) E O, fl denotes a boullded region in R", 0fl signifies a boundary of fl forclass C' …    

2.  ATTRACTOR AND DIMENSION FOR STRONGLY DAMPED NONLINEAR WAVE EQUATION  
   周盛凡《应用数学学报(英文版)》,2000年第16卷第3期
   1. IntroductionConsider the strongly damped nonlinear wave equationwith the Dirichlet boundary conditionand the initial value conditionswhere u = u(x, t) is a real--valued function on fi x [0, co), fi is an open bounded set of R"with smooth boundary off, or > 0, g e L'(fl), D(--Q) ~ Ha(~~) n H'(fl).We assume for the function f(u) as follows'f(u) E CI (R, R) satisfiesfor any ig al, uZ E R, where k, hi > 0, i ~ 0, 1, 2, 61 > 0 and 0 5 6o < 1'The type of equation (1) can be regarded as the…    

3.  A CLASS OF NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION  被引次数:23
   莫嘉琪《应用数学学报(英文版)》,2001年第17卷第4期
   The author discussed a class of singularly perturbed problems for differential equation fiee {1--7]). Now we consider the non1ocal singu1arly perturbed problem as follows:where E is a positive small parameter anHere x = (xl, x2,' ) x.) E n, fl denotes a bounded region in R", 0fl signilies a boundary offl for class Cl cr (cr 6 (0, 1) is H5lder exponent), T0 is a positive constant, L1 is a uniformlyelliptic operator, L2 is a first order differential operator, T is an integral operator, K(x…    

4.  A GENERALIZATION OF LEBESGUE DIFFERENTIAL THEOREM AND ITS APPLICATION  被引次数:1
   周振荣《数学物理学报(B辑英文版)》,2001年第1期
   1 IntroductionLet fl C Rn. Classical Lebesgue differential theorem says:u(x) = liny IB.(x)l--' j u(y)dy a.e. in fl Vu E L'(fl),r-o js.(.)"(y)dy a.e. in fl Vu E L'(fl),where, Br(x) is the euclidean metric ball witl1 radius r and center x; IB.(x)I is the Lebesguemeasure of B.(x). Taking use of it, one can deduce Canpanato's integral chaxacterization ofH5lder continuous f[1nctions and Morrey's growing theorem of Dirichlet integration which playan imPortant role in regularity theories of …    

5.  球上一类含临界增长p-Laplace方程的渐近性(英文)  
   耿堤   薛亚芬《Annals of Differential Equations》,2002年第1期
   1 IntroductionIn this paper we study the blow--up of positive solutions as A - 0+ fOr thefOllowing boundary value problem of the weighted pLaplacian on the unit ballcenter at the origin B = B1(0) C Rn:where cr5 u > fi --p > --n and p* = p(n + a)/(fi +n --p) is the critical exponentof the embedding Wl"(fl, lxtpdx) - Lp*(fl, lxl"dx) (see, for example, [6]).When u is radially symmetric, y(r) = u(x), fOr r = lxl, satisfieswhere the new exponents cr, g, p and p* satisfyThe existence and non-exi…    

6.  EXISTENCE OF MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS  
   谢资清  肖海军《数学物理学报(B辑英文版)》,2001年第1期
   1 IntroductionWe deal with the problem{ it:;,.""--'"'::3of (11)where 9 C RN, N 2 3 is a bounded domain with smooth boundary 0fl, 0n = ro U r1, ro andYl have (N -- 1)-dinlensiollal Hausdorff nleasuret r E L'(r1), yt 2 0, V * 0 on r1, 7 denotesthe u11it outward normal and p = 2* = ee is the critical SoboleY exponent fOr the Sobolevembedding V(O) - H(O), V(fl) = {u E H'(fl) l u = 0 on ro}'The case ro and r1 have positive (N -- 1)-dimellsional Hausdoor measure aud p = 0on r1 in (1.1), has…    

7.  STATIONARY STRUCTURES FOR A WEAKLY COUPLED ELLIPTIC SYSTEM ARISING IN TWO-PREDATOR, TWO-PREY MODELS  
   严平  林支桂《数学物理学报(B辑英文版)》,2001年第4期
   1 IntroductionIn tl1is paper we coIlsider positive steady-statc solutiolls to the fOllowi1lg weakly-c()uI)ledparabolic systenlwllere fl is a bouuded don1ain in Rn with sufficiently smooth bouudary, t1T = n x [0, T) and0f1T = 0fl x [0, T) l' is the olltward ul1it 11orIIlaJ vector. The col1stants ai, bi, (i = 1. 2, 3, 4, j =l, 2, 3, 4) are positive.The systenl (1.1) describes tlle LotkaVOlterra two-predator, two-prey nlodcl. u1 a11d u2represeIlt tl1e del1sitie8 of twDeprey wllile u3, '('4 …    

8.  INITIAL-BOUNDARY VALUE PROBLEM FOR THE UNSATURATED LANDAU-LIFSHITZ SYSTEM  
   DING Shijin  GUO Boling《数学年刊B辑(英文版)》,2000年第21卷第3期
   51. IntroductionLet fi C Re (n = 1,2) be a bounded smooth domain. Consider the following nonhomogeneous initial-boundary value problem for the unsaturated Landau-Lifshitz systems offerromagnetic spin chain with Gilbert damping constant afl > 0,where adZ is the exchange constallt, u = (u', u', u'), "o(x) is smooth and satisfies the unsaturated condition, i.e., Ilo(~)I gi constant, and in IVuol' < co, "o(x)IOn = op(x). DenoteW(x) = luo(x)I. We assume 0 < m = mane < M ~ mpxW. Throughout t…    

9.  OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES  
   汪更生《数学物理学报(B辑英文版)》,2001年第4期
   1 IntroductionThroughout this paPer, we denote n an opell bounded domain in Rn with smooth boulldary0fl, let Q = fl x (0,T) and r = 0n x (0,T). Let H = L'(n).We shall study the optimal control problems governed by the following system:y'(t) Ay(t) p(y(t) -- rk(t)) 9 B1u(t) I1(t), (1.1)y(0) = u0,rk'(t) Aop(f) 7(op(f)) = B2u(t) f2(f), (1.2)op(0) = op0with the state constrchtF(y) C W' (1.3)The pay-off functional is given byJ(y, u) = l"[,(,, y) h(u)]dt. (1.4)JoNote that y' and…    

10.  POSITIVE THIN PLATE SPLINES  
   FlorencioI.Utreras《分析论及其应用》,1985年第3期
   We consider the problem of interpolating positive data at scat-tered data points of the plane R~2. To solve the problem, weintroduce the Positive Thin Plate Spline, i. e. the solution to Minimize integral from n=R~2{x~2/~2u}~2 + 2{xy/~2u}~2 + {y~2/~2u}~2, u ∈ D~(-2)L~2(R~2); u(t_j) = z_j, j=1…, n; u(t)≥0, t∈ Kwhere (t_j, z_j) are the data, K is a convex compact subset of R~2.We give existence, uniqueness, characterisation and convergenceresults. We also present a dual algorithm to compute this splineand show numerical experience with the method.    

11.  POSITIVE THIN PLATE SPLINES  
   FlorencioI.Utreras《分析论及其应用》,1985年第3期
   We consider the problem of interpolating positive data at scat-tered data points of the plane R~2. To solve the problem, weintroduce the Positive Thin Plate Spline, i. e. the solution to Minimize integral from n=R~2{x~2/~2u}~2 + 2{xy/~2u}~2 + {y~2/~2u}~2, u ∈ D~(-2)L~2(R~2); u(t_j) = z_j, j=1…, n; u(t)≥0, t∈ Kwhere (t_j, z_j) are the data, K is a convex compact subset of R~2.We give existence, uniqueness, characterisation and convergenceresults. We also present a dual algorithm to compute this splineand show numerical experience with the method.    

12.  SINGULAR PERTURBATION OF NONLINEAR BOUNDARY VALUE PROBLEMS  
   章国华  林宗池《应用数学和力学(英文版)》,1984年第5卷第5期
   In this paper we consider the boundary value problem where ε.μ are two positive parameters. Under f_y≤-k<0 and other suitable restrictions, there exists a solution and it satisfied where y_(0,0)(x) is solution of reduced problem while y_i-j,j(x)(j=0,1,...,i;i=1,2,...,m) can be obtained successively from certain linear equations.    

13.  A SINGLE STEP SCHEME WITH HIGH ACCURACY FOR PARABOLIC PROBLEM  
   陈传淼  胡志刚《数学物理学报(B辑英文版)》,2001年第2期
   1 IntroductionConsider one-dimellsional parabolic problem in fl = (0, 1)and its weak formulatioll: find u(t) E S0 = {v 6 H'(fl), v(0) = 0} 8uch thatwhere the coefficients a(x) and b(x) are independent of t, Au = --(au')' ha, a(x) 2 ao > 0, b 20, and bilinear fOrm A(u, v) = fol(au'V' buv)dx i8 So-coercive, i.e. A(u, v) 2 ullu1li, u ESO, u > 0.Make in n = (0, 1) a subdivision: xo = 0 < x1 < x2 <.' < xn = 1. Set an elenlentry = (xj--l, xj), nddpoint xj--1/2 = (ry n--1)/2 and steplengt…    

14.  ASYMPTOTIC FORMULAE OF EIGENVALUE-COUNTING FUNCTION FOR ELLIPTIC EIGENVALUE PROBLEMS ON A BOUNDED DOMAIN WITH A FRACTAL BOUNDARY  
   Minoru Yanagawa  王忠  孙炯《Annals of Differential Equations》,2002年第2期
   IIntroductlonLet fi be a bounded open set In the n-dimensional Euclldean space R”withtheboundaryo0.In this paper,we shallessentiallydeal with thefollowingeigenvalue problem:,nD 一)。o…4km)螂川川J”人川川,x〔u,丸 人k=1\“’“)llillj=U.U b UI[。where丸 meanso/axj,and we suPPose that coeaclents aj。(x),J;k= 1,2;…,。satisfy the following conditions:(1)aj。(x)is real function and belong to Cm(R”);(2)There exists an M>0;such that Iajk(x)l<M;;;k二 1,2,…,n;148 Ann ofDiff Eqs Vol…    

15.  OPTIMAL CONTROL PROBLEM OF PARABOLIC DIFFERENTIAL EQUATIONWITH TWO POINT BOUNDARY CONDITION  
   汪更生  刘昌良《数学物理学报(B辑英文版)》,1999年第19卷第2期
   1IntroductionLetfibeaboundeddomainOfR"withsmoothboundaryoff,KCL'(fl)xL'(fl)beasubsetdefinedasfollows:K={(yi,yi)EL'(fl)xL'(fl);yi(x) p(yl(x))30,a.e.infi},(1)withwhichisamaximalmonotonegraphonRxR.Whereaisapositiveconstant.Ourmainproblemisasfollows:(O)MinimizeL(y,u)={'[g(y(t)) h(u(t))]at,overallpairssubjecttotheconditionsOurbasichypothesesaboutgandharethefollowing:(H)Bothgandh:L'(fl)~(--co, co]arelowersendcontinuous,convexsproperfunctionals,withg(y)    

16.  IDENTIFICATION OF PARAMETERS IN SEMILINEAR PARABOLIC EQUATIONS  
   刘振海《数学物理学报(B辑英文版)》,1999年第2期
   1IntroductionWeconsiderthefollowingsystem:notu--Z0',(a(x)ox.u)=f(x,t,u),(x,t)EQ,i=1,u(x,t)=0,(x,t)ES,(1)u(x,0)=u000,xEfi,wherefiisaboundeddomaininR"(n21),Q={(x,t):xEfi,tE(0,T)}with0    

17.  Oblique derivative problem for general Chaplygin-Rassias equations  
   WEN GuoChun LMAM  School of Mathematical Sciences  Peking University  Beijing 100871  China《中国科学A辑(英文版)》,2008年第51卷第1期
   The present paper deals with the oblique derivative problem for general second order equations of mixed (elliptic-hyperbolic) type with the nonsmooth parabolic degenerate line K_1(y)u_(xx) |K_2(x)|u_(yy) a(x,y)u_x b(x, y)u_y c(x,y)u=-d(x,y) in any plane domain D with the boundary D=Γ∪L_1∪L_2∪L_3∪L_4, whereΓ(■{y>0})∈C_μ~2 (0<μ<1) is a curve with the end points z=-1,1. L_1, L_2, L_3, L_4 are four characteristics with the slopes -H_2(x)/H_1(y), H_2(x)/H_1(y),-H_2(x)/H_1(y), H_2(x)/H_1(y)(H_1(y)=|k_1(y)|~(1/2), H_2(x)=|K_2(x)|~(1/2) in {y<0}) passing through the points z=x iy=-1,0,0,1 respectively. And the boundary condition possesses the form 1/2 u/v=1/H(x,y)Re[λuz]=r(z), z∈Γ∪L_1∪L_4, Im[λ(z)uz]|_(z=z_l)=b_l, l=1,2, u(-1)=b_0, u(1)=b_3, in which z_1, z_2 are the intersection points of L_1, L_2, L_3, L_4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations K_1(y)(M_2(x)u_x)_x M_1(x)(K_2(y)u_y)_y r(x,y)u=f(x,y), in D as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K(y)u_(xx) u_(yy)=0 with the boundary condition u(z)=φ(z) onΓ∪L_1∪L_4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for the general Chaplygin- Rassias equations are proved. The used method in this paper is different from those in other papers, because the new notations W(z)=W(x iy)=u_z=[H_1(y)u_x-iH_2(x)u_y]/2 in the elliptic domain and W(z)=W(x jy)=u_z=[H_1(y)u_x-jH_2(x)u_y]/2 in the hyperbolic domain are introduced for the first time, such that the second order equations of mixed type can be reduced to the mixed complex equations of first order with singular coefficients. And thirdly, the advantage of complex analytic method is used, otherwise the complex analytic method cannot be applied.    

18.  The Exterior Tricomi and Frankl Problem  
   JohnM.Rassias《数学研究与评论》,1990年第4期
   F. G. Tricomi (1923—), S. Gellerstedt (1935—), F.I.Frankl (1945—),A. V. Bitsadze and M. A. Lavrentiev (1950—), M. H. Protter (1953—) and most of the recent workers in the field of mixed type boundary value problems have considered only one parabolic line of degeneracy. The problem with more than one parabolic line of degeneracy becomes more complicated. The above researchers and many others have restricted their attention to the Chaplygin equation:K(y)·u_(xx)+u_(yy)=f(x, y) and not considered the "generalized Chaplygin equation:"Lu=K(y)·u_(xx)+u_(yy)+r(x, y)·u=f(x, y) because of the difficulties that arise when r:=non-trivial (≠0). Also it is unusual for anyone to study such problems in a doubly connected region. In this paper 1 consider a case of this type with two parabolic lines of degeneracy, r:= non-(?)≠(?), in a doubly connected region,and such that boundary conditions are presenbed only on the "exterior boundary" of the mixed domain, and Ⅰobtam uniqueness (?) for quasllegular solutions    

19.  The 3D Inverse Problem of the Wave Equation for a General Multi-connected Vibrating Membrane with a Finite Number of Piecewise Smooth Boundary Conditions  
   E. M. E. ZAYED《数学学报(英文版)》,2005年第21卷第4期
   The trace of the wave kernel μ(t) =∑ω=1^∞ exp(-itEω^1/2), where {Eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 (δ/δxk)^2 in the (x^1, x^2, x^3)-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ (t) on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j (j = 1,……, n), where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^* (i = 1 + kj-1,……, kj) of the bounding surfaces S j are considered, such that S j = Ui-1+kj-1^kj Si^*, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω (e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature) are determined from the asymptotic expansion ofexpansion of μ(t) for small │t│.    

20.  SINGULAR PERTURBATION FOR A CLASS OF SEMILINEAR SECOND ORDER SYSTEMS WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR  
   章国华  林宗池《数学物理学报(B辑英文版)》,1985年第2期
   We study the boundary value problem where ε, μ are two positive parameters, are n-dimensional vector functions and the boundary is perturbed. This vector boundary problem does not appear to have been studied. Under appropriate assumptions we obtain existence of solution and satisfies where i=1, 2, …, n; Here y_(0,0)~t(t) is a solution of reduced equation f~i (t, y~1, …, y_(0,0)~t,…, y~n, 0, 0)=0, while y_(s-k,k)~i(t) (k=0, 1,…, s; s=1, 2, …, m) can be obtained successively from certain linear systems.    

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