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Journal of the Korean Mathematical Society
Journal Basic Information
pISSN :
0304-9914
eISSN :
2234-3008
Journal DOI :
10.4134/JKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
Volume & Issues
Volume 37, Issue 6 - Nov 2000
Volume 37, Issue 5 - Sep 2000
Volume 37, Issue 4 - Jul 2000
Volume 37, Issue 3 - May 2000
Volume 37, Issue 2 - Mar 2000
Volume 37, Issue 1 - Jan 2000
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1
FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES
Park, Se-Hie ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 885~899
Abstract
We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.
2
THE INDEX FOR A TOPOLOGICAL DEGREE THEORY FOR DENSELY DENIED OPERATORS OF TYPE
IN BANACH SPACES
Kartsatos, Athanassios G. ; Skrypnik, Igor V. ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 901~913
Abstract
This is a summary of results involving the development of a theory of an index of an isolated critical point for densely defined nonlinear operators of type (S(sub)+)(sub)0,L. This index theory is associated with a degree theory, for such operators, whch has been recently developed by the authors.
3
DEGENERATE VOLTERRA EQUATIONS IN BANACH SPACES
Favini, Angelo ; Tanabe, Hiroki ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 915~927
Abstract
This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k(
) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where
is a pole for (
L + M)(sup)-1.
4
LOCAL AND NORM BEHAVIOR OF BLOWUP SOLUTIONS TO A PARABOLIC SYSTEM OF CHEMOTAXIS
Senba, Takasi ; Suzuki, Takashi ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 929~941
Abstract
We study a parabolic system of chemotaxis introduced by E.F. Keler and L.A. Segel. First, norm behaviors of the blow-up solution are proven. Then some kind of symmetry breaking and the concentration toward the boundary follow when the L
norm of the initial value is less than 8
. Meanwhile a method of rearrangement is porposed toprove an inequality of Trudinger-Moser's type.
5
INFINITELY MANY SOLUTIONS OF A WAVE EQUATION WITH JUMPING NONLINEARITY
Park, Q-Heung ; Jung, Tack-Sun ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 943~956
Abstract
We investigate a relation between multiplicity of solutions and source terms of jumping problem in wave equation when the nonlinearity crosses an eigenvalue and the source term is generated by finite eigenfunctions. We also show that the jumping problem has infinitely many solutions when the source term is positive multiple of the positve eigenfunction.
6
REGULARITY AND SINGULARITY OF WEAK SOLUTIONS TO OSTWALD-DE WAELE FLOWS
Bae, Hyeong-Ohk ; Choe, Hi-Jun ; Kim, Do-Wan ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 957~975
Abstract
We find a regularity criterion for the Ostwald-de Waele models like Serrin's condition to the Navier-Stokes equations. Moreover, we show short time existence and estimate the Hausdorff dimension of the set of singular times for the weak solutions.
7
STANDING WAVE SOLUTIONS FOR THE PLANER CHERN-SIMONS GAUGED NONLINEAR SCHRODINGER EQUATION WITH AN EXTERNAL ELECTROMAGNETIC FIELD
Kurata, Kazuhiro ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 977~989
Abstract
In this paper we construct a standing solitary wave solution with prescribed total electric charge to the planer Chern-Simons gauged nonlinear Schrodinger equation with an external electromagnetic field by using a variations method.
8
ON SCATTERING BY SEVERAL OCNVEX BODIES
Ikawa, Mitsuru ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 991~1005
Abstract
We consider a zeta function of the classical dynamics in the exterior of several convex bodies. The main result is that the poles of the zeta function cannot converge to the line of absolute convergence if the abscissa of absolute convergence of the zeta function is positive.
9
REMARKS ON UNIQUENESS AND BLOW-UP CRITERION TO THE EULER EQUATIONS IN THE GENERALIZED BESOV SPACES
Ogawa, Takayoshi ; Taniuchi, Yasushi ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 1007~1019
Abstract
In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.
10
SYMMETRIC DUALITY FOR NONLINEAR MIXED INTEGER PROGRAMS WITH A SQUARE ROOT TERM
Kim, Do-Sang ; Song, Young-Ran ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 1021~1030
Abstract
We formulate a pair of symmetric dual mixed integer programs with a square root term and establish the weak, strong and converse duality theorems under suitable invexity conditions. Moreover, the self duality theorem for our pair is obtained by assuming the kernel function to be skew symmetric
11
ON THE BOUNDARY VALUE PROBLEMS FOR LOADED DIFFERENTIAL EQUATIONS
Dzhenaliev, Muvasharkhan T. ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 1031~1042
Abstract
The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.
12
FOURIER-BESSEL TRANSFORMATION OF MEASURES WITH SEVERAL SPECIAL VARIABLES AND PROPERTIES OF SINGULAR DIFFERENTIAL EQUATIONS
Muravnik, A.B. ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 1043~1057
Abstract
This paper is devoted to the investigation of mixed Fourier-Bessel transformation (※Equations, See Full-text) We apply the method of [6] which provides the estimate for weighted L(sub)
-norm of the spherical mean of │f│
via its weighted L
-norm (generally it is wrong without the requirement of the non-negativity of f). We prove that in the case of Fourier-Bessel transformatin the mentioned method provides (in dependence on the relation between the dimension of the space of non-special variables n and the length of multiindex ν) similar estimates for weighted spherical means of │f│
, the allowed powers of weights are also defined by multiindex ν. Further those estimates are applied to partial differential equations with singular Bessel operators with respect to y
, …, y(sub)m and we obtain the corresponding estimates for solutions of the mentioned equations.
13
BOUNDARY REGULARITY TO THE NAVIER-STOKES EQUATIONS
Bae, Hyeong-Ohk ; Kim, Do-Wan ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 1059~1070
Abstract
Under the critical assumption that ▽u
L(sub)loc(sup)
,
, 3/
+ 2/
2 with
3/2, a boundary L(sup)
estimate for the solution is derived if the pressure on the boundary is bounded. Here, our estimate is local.
14
ANALYTIC SMOOTHING EFFECT AND SINGLE POINT SINGULARITY FOR THE NONLINEAR SCHRODINGER EQUATIONS
Kato, Keiichi ; Ogawa, Takayoshi ;
Journal of the Korean Mathematical Society, volume 37, issue 6, 2000, Pages 1071~1084
Abstract
We show that a weak solution of the Cauchy problem for he nonlinear Schrodinger equation, {i∂(sub)t u + ∂
(sub)x u = f(u,u), t∈(-T,T), x∈R, u(0,x) = ø(x).} in the negative solbolev space H(sup)s has a smoothing effect up to real analyticity if the initial data only have a single point singularity such as the Dirac delta measure. It is shown that for H(sup)s (R)(s>-3/4) data satisfying the condition (※Equations, See Full-text) the solution is analytic in both space and time variable. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [18] and previous work by Kato-Ogawa [12]. We give an improved new argument in the regularity argument.