LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

We obtain a local regularity result for solutions to Kψ,θ-obstacle problem of A-harmonic equation divA(x,u(x),▽u(x))=0,where A:Ω× R×Rn → Rn is a Carath'eodory function satisfying some coercivity and growth conditions with the natural exponent 1pn,the obstacle function ψ≥0,and the boundary data θ∈W1,p(?).     

关于一阶具分布型偏差变元微分方程的振动性

In this paper we study the oscillation of the retarded differential equation x′(t)+∫_a^bp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (1)and the advanced differential equation x′(t)-∫_a^bp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (2) We improved the main results of [1-4].     

OBSTACLE PROBLEMS FOR SCALAR GINZBURG-LANDAU EQUATIONS

In this note, we establish some estimates of solutions of the scalar Ginzburg-Landau equation and other nonlinear Laplacian equation △u =f(x, u). This will give an estimate of the Hausdorff dimension for the free boundary of the obstacle problem.     

On 2n—th—Order Eigenvalue Problem

In [1], Lu discussed the existence of positive solution for the BVPwhere f: [0, 1] × [0, ∞) → R is continuous and satisfies the following conditions(H1) There exists an M > 0 such that(H2) limx→∞ f(t, x)/x =∞uniformly for t [α,β] (0, 1) for some α < β and λ > 0 is a parameter.In this paper, the result of [1] is generalized to the following 2n-th-order BVPThe result of this paper isTheorem 1 Assume (H1) and (H2) hold. Then the BVP (3)-(4) has a positive solutionifλ > 0 is sm…     

Solution to Nonlinear Parabolic Equations Related to the P-Laplacian

Consider the following Cauchy problem:u_t = div(|▽u ~m |~ p-2▽u~m),(x,t) ∈ST=R~N ×(0,T),u(x,0) = μ,x ∈R~N,where 1相似文献   

On Critical Fujita Exponents for a Degenerate Parabolic Equation With

Our interest is to determine the critical Fujita exponent concerned withthe following initial-boundary value problem ut= Δum, x ∈RN+, t>0, (1) u(x,0)=u0(x), x∈RN+, (2) -(um)/(x1)=up, x1=0, t>0, (3) where RN+=(x1, x′)| x′∈R{N-1, x1>0,m>1, p>0, and u0(x) is a nonnegative bounded function with compact supportsatisfying thecompatibility condition -(um0(x))/(x1)=up0(x), x1=0. We call p0 the critical global existence exponent if ithas the following property: if p>p0, there always exist nonglobalsolutions of the problem (1)--(3) while if 0pc small data solutionsexist globally in time while large data solutions are nonglobal.     

ON UNIFORM ASYMPTOTIC STABILITY OF INFINITE DELAY DIFFERENCE EQUATIONS

51. IntroductionThe aim of thi8 paPer is to establish the stability criteria for the indnite de1ay differenceequations of the formx(n 1) = F(n,x.) for n E Z, (1'l)where F: Z x CH -- Rk, Z denotes the integer set, Rh is the n-dimensional Euclidean space,CH = {T E C: llWII < H} fOr some constan H > 0, whileC = {yt: {... l --2, --1,0} - Rk l W is bounded}withllytIl = sup IW(8)I for W E C,8<0and x.(8) = x(n 8) for 8 5 0. Here, and in the sequel, l' I is a norm in Rk, and we atwa…     

DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL HALF SPACE

This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t > 0, x = (x 1 , x ′ ) ∈ R n + := R + × R n 1 , u(0, x) = u 0 (x) → u + , as x 1 → + ∞ , u t (0, x) = u 1 (x), u(t, 0, x ′ ) = u b , x ′ = (x 2 , x 3 , ··· , x n ) ∈ R n 1 . (I) For the non-degenerate case f ′ 1 (u + ) < 0, it was shown in [10] that the above initialboundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave φ(x 1 ) uniformly in x 1 ∈ R + as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t → + ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ (u) < 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 (u b ) ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.     

INSTANTANEOUS SHRINKING AND LOCALIZATION OF FUNCTIONS IN Yλ （m,p,q,N） AND THEIR APPLICATIONS

61. IntroductionAs well knoWn, the solutionS of semilinear Parabolic equations at = An -- ac, 0 < q < 1have the ISS (the thetantaneous shrinking of the support) ~erty (see 11--5]).Such PrOPerty is d~d as follows.Defiallion 1.1. A hoction u E La(Q) is sold to haw the ISS p~rty, ijjor augr > 0, there hots a POsiboe n~ber R = R(T) such thatu(z, t) = 0for a. e. (z,t) e (R" \ Ba) x (T, co), tDhere AN is the N-dimensional Euclidean space,and Q = AN X (0, co).UP to the preseDt, there…     

EXISTENCE AND UNIQUENESS OF BV SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH DIRAC MEASURE AS SOURCES

The aim of this paper is to discuss the existence and uniqueness ofsolutions for the porous medium equation ut-(u^m)xx=μ（x） in （x，t）∈R&#215;（0，+∞） with initial condition u(x,0)=u0(x) x∈（-∞，+∞），where μ(x) is a nonnegative finite Radon measure, u0∈L^1 (R)∩L^∞ (R) is a nonnegative function, and m&gt;1, and R≡(-∞, +∞).     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.