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1.
The following regularity of weak solutions of a class of elliptic equations of the form are investigated.  相似文献   

2.
The authors localize the blow-up points of positive solutions of the systemu t u,v t v with conditions at the boundary of a bounded smooth domain Θ under some restrictions off andg and the initial data (Δu 0, Δν0>c>0). If Θ is a ball, the hypothesis on the initial data can be removed. Supported by Universidad de Buenos Aires under grant EX071 and CONICET.  相似文献   

3.
§1IntroductionInthepaper,weconsidertheinitialandboundaryvalueproblemasfolows:ut=Δ(gradφ(u))+αΔb(u)+f(x,t,u),(x,t)∈QT=Ω×(0,T](...  相似文献   

4.
In this note, we will give another proof of the uniqueness of mild solutions to the Navier-Stokes equations in the class C([0,∞); by a simple application of Giga-Shor’s L p L q (time-space) estimates, i.e., integral norms in the time variable. The proof relies on a method introduced by S. Monniaux [9] to prove the same result. Received: 11 June 2006  相似文献   

5.
This paper presents a row relaxation method for solving the doubly regularized minimax problem
  相似文献   

6.
In this paper, a new criterion of the non-existence of periodic solutions for a generalized liénard system
is given, which generalizes and extends some known results of Sugie et al. The results can be applied to the well-known nonlinear oscillating equation +f(x)h()+g(x)k()=0, and the criterion of the non-existence of periodic solutions associated with this equation is obtained.  相似文献   

7.
The asymptotic behavior of viscosity solutions to the Cauchy–Dirichlet problem for the degenerate parabolic equation u t  = Δ u in Ω × (0,∞), where Δ stands for the so-called infinity-Laplacian, is studied in three cases: (i) and the initial data has a compact support; (ii) Ω is bounded and the boundary condition is zero; (iii) Ω is bounded and the boundary condition is non-zero. Our method of proof is based on the comparison principle and barrier function arguments. Explicit representations of separable type and self-similar type of solutions are also established. Moreover, in case (iii), we propose another type of barrier function deeply related to a solution of . Goro Akagi was supported by the Shibaura Institute of Technology grant for Project Research (no. 2006-211459, 2007-211455), and the grant-in-aid for young scientists (B) (no. 19740073), Ministry of Education, Culture, Sports, Science and Technology. Petri Juutinen was supported by the Academy of Finland project 108374. Ryuji Kajikiya was supported by the grant-in-aid for scientific research (C) (no. 16540179), Ministry of Education, Culture, Sports, Science and Technology.  相似文献   

8.
We consider here a class of nonlinear Dirichlet problems, in a bounded domain , of the form
investigating the problem of uniqueness of solutions. The functions (s) and satisfy rather general assumptions of locally Lipschitz continuity (with possibly exponential growth) and the datum f is in L1(). Uniqueness of solutions is proved both for coercive a(x, s) and for the case of a(x, s) degenerating for s large.  相似文献   

9.
We prove existence of continuous solutions for
, where γ is a maximal monotone graph, by showing equicontinuity of a sequence of approximate solutions. Relations of this type are models for certain free boundary problems like the Stefan problem with nonlinear diffusion. Entrata in Redazione il 17 dicembre 1998. Research supported by CMUC-FCT, Praxis XXI and project Praxis/2/2.1/MAT/125/94.  相似文献   

10.
In this article we analyze viscosity solutions of the one phase Hele-Shaw problem in the plane and the corresponding free boundaries near a singularity. We find, up to order of magnitude, the speed at which the free boundary moves starting from a wedge, cusp, or finger-type singularity. Maximum principle-type arguments play a key role in the analysis.  相似文献   

11.
In this paper, the existence of travelling front solution for a class of competition-diffusion system with high-order singular point
(I)
is studied, where d i,ai>0 (i=1,2) and w=(w 1(x,t),w 2(x,t)). Under the certain assumptions on f, it is showed that if a i<1 for some i, then (1) has no travelling front solution, if a i≥1 for i=1,2, then there is a c 0,c*>0, where c* is called the minimal wave speed of (I), such that if cc 0 or c=c*, then (I) has a travelling front solution, if c<c*, then (I) has no travelling front solution by using the shooting method in combination with a compactness argument. Project supported by both the National (49772161) and Henan Province (984050300) Natural Science Foundations of China.  相似文献   

12.
We are interested in parabolic problems with L1 data of the type
with i, j=0, 1, (i, j) (0, 0), 0 = 0 and 1 = 1. Here, is an open bounded subset of with regular boundary and is a Caratheodory function satisfying the classical Leray-Lions conditions and is a monotone graph in with closed domain and such that We study these evolution problems from the point of view of semi-group theory, then we identify the generalized solution of the associated Cauchy problem with the entropy solution of in the usual sense introduced in [5].  相似文献   

13.
We show the existence of absolutely continuous extremal solutions to the problemx′(t)=f(t, x)h(t)))+g(t)),x(0)=x 0, whereh is an arbitrary continuous deviated argument. Conditions for the uniqueness of solutions are given. Research partialy supported by grant UG BW 5100 - 5 - 0143 - 4  相似文献   

14.
A tree T is called a k-tree, if the maximum degree of T is at most k. In this paper, we prove that if G is an n-connected graph with independence number at most n + m + 1 (n≥1,nm≥0), then G has a spanning 3-tree T with at most m vertices of degree 3.  相似文献   

15.
Sign changing solutions of semilinear elliptic problems in exterior domains   总被引:1,自引:0,他引:1  
We prove the existence of a sign changing solution to the semilinear elliptic problem , in an exterior domain Ω having finite symmetries.  相似文献   

16.
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied.  相似文献   

17.
We consider the 2-D Keller-Segel system (KS) for γ > 0. We first construct a mild solution of (KS) for every . The local existence time is characterized for with 1 < q * < 2. Next, we prove the finite time blow-up of strong solution under the assumption and , where g(s) is an increasing function of s > 1 with an explicit representation. As an application of our mild solutions, an exact blow-up rate near the maximal existence time is obtained.   相似文献   

18.
We adapt to degenerate m-Hessian evolution equations the notion of m-approximate solutions introduced by N. Trudinger for m-Hessian elliptic equations, and we present close to necessary and sufficient conditions guaranteeing the existence and uniqueness of such solutions for the first initial boundary value problem. Dedicated to Professor Felix Browder  相似文献   

19.
This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe (Numer Math 68:95–106, 1994) that combines projected Gauss–Seidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely ill-conditioned problems. Numerical tests indicate that the approach is more efficient than interior-point and gradient projection methods on some physical simulation problems that arise in computer game scenarios. The research of J. L. Morales was supported by Asociación Mexicana de Cultura AC and CONACyT-NSF grant J110.388/2006. The research of J. Nocedal was supported by National Science Foundation grant CCF-0514772, Department of Energy grant DE-FG02-87ER25047-A004 and a grant from the Intel Corporation.  相似文献   

20.
In this paper we study a nonlinear elliptic differential equation driven by thep-Laplacian with a multivalued boundary condition of the Neumann type. Using techniques from the theory of maximal monotone operators and a theorem of the range of the sum of monotone operators, we prove the existence of a (strong) solution.  相似文献   

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