共查询到20条相似文献，搜索用时 15 毫秒
1.
Frances Hammock Peter Luthy Alexander M. Meadows Phillip Whitman 《Proceedings of the American Mathematical Society》2007,135(5):1419-1430
We show partial regularity of bounded positive solutions of some semilinear elliptic equations in domains of . As a consequence, there exists a large variety of nonnegative singular solutions to these equations. These equations have previously been studied from the point of view of free boundary problems, where solutions additionally are stable for a variational problem, which we do not assume.
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《偏微分方程通讯》2013,38(1-2):121-138
Abstract In this paper we are interested in a free boundary problem with a motion law involving the mean curvature term of the free boundary. Viscosity solutions are introduced as a notion of global-time solutions past singularities. We show the comparison principle for viscosity solutions, which yields the existence of minimal and maximal solutions for given initial data. We also prove uniqueness of the solution for several classes of initial data and discuss the possibility of nonunique solutions. 相似文献
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G. Gripenberg 《Journal of Mathematical Analysis and Applications》2009,352(1):175-183
Sufficient conditions are given for the solutions to the (fully nonlinear, degenerate) elliptic equation F(x,u,Du,D2u)=0 in Ω to satisfy |u(x)−u(y)|?Cα|x−y| for some α∈(0,1) when x∈Ω and y∈∂Ω. 相似文献
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Luis Caffarelli Arshak Petrosyan Henrik Shahgholian 《Journal of the American Mathematical Society》2004,17(4):827-869
We study the regularity of the free boundary in a Stefan-type problem
with no sign assumptions on and the time derivative .
with no sign assumptions on and the time derivative .
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Ravi P. AgarwalHaishen Lü Donal O'Regan 《Journal of Mathematical Analysis and Applications》2002,266(2):383-400
We consider the boundary value problem (?p(u′))′ + λF(t, u) = 0, with p > 1, t ∈ (0, 1), u(0) = u(1) = 0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed. 相似文献
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袁光伟 《数学物理学报(B辑英文版)》1995,15(3):247-253
ＲＥＧＵＬＡＲＩＴＹＯＦＴＨＥＦＲＥＥＢＯＵＮＤＡＲＹＩＮＥＬＥＣＴＲＯＣＨＥＭＩＣＡＬＭＡＣＨＩＮＩＮＧＰＲＯＢＬＥＭＹｕａｎＧｕａｎｇｗｅｉ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓ... 相似文献
9.
《数学物理学报(B辑英文版)》1995,15(3)
The \"hole-boring problem\" in ECM is considered.It is shown that after a finite period of time the free boundary becomes smooth in space variables and Holder continuous in time variable without imposing specific geometric assumption on the initial and boundary data. 相似文献
10.
Andreas Poullikkas Andreas Karageorghis Georgios Georgiou John Ascough 《Numerical Methods for Partial Differential Equations》1998,14(5):667-678
We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667–678, 1998 相似文献
11.
Penelope Smith 《Journal of Mathematical Analysis and Applications》2006,316(2):483-494
In part I (P. Smith, Perron's method for quasilinear hyperbolic systems, part I, J. Math. Anal., in press) of this paper we defined a notion of viscosity solution (sub- (super-)solution) for these systems, proved a comparison principle for viscosity sub- and supersolutions. Here, in part II, we prove existence of viscosity solutions to the Cauchy problem, using a Perron-like method, for long time, and for all time. 相似文献
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Emmanouil Milakis 《偏微分方程通讯》2013,38(8):1227-1252
We obtain local C α, C 1,α, and C 2,α regularity results up to the boundary for viscosity solutions of fully nonlinear uniformly elliptic second order equations with Neumann boundary conditions. 相似文献
16.
Francesca Da Lio 《Journal of Mathematical Analysis and Applications》2008,339(1):384-398
In this paper we are interested in the large time behavior as t→+∞ of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linèaire 22 (5) (2005) 521-541]. 相似文献
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We propose a new numerical method for the solution of the Bernoulli free boundary value problem for harmonic functions in a doubly connected domain D in where an unknown free boundary Γ0 is determined by prescribed Cauchy data on Γ0 in addition to a Dirichlet condition on the known boundary Γ1. Our main idea is to involve the conformal mapping method as proposed and analyzed by Akduman, Haddar, and Kress for the solution of a related inverse boundary value problem. For this, we interpret the free boundary Γ0 as the unknown boundary in the inverse problem to construct Γ0 from the Dirichlet condition on Γ0 and Cauchy data on the known boundary Γ1. Our method for the Bernoulli problem iterates on the missing normal derivative on Γ1 by alternating between the application of the conformal mapping method for the inverse problem and solving a mixed Dirichlet–Neumann boundary value problem in D. We present the mathematical foundations of our algorithm and prove a convergence result. Some numerical examples will serve as proof of concept of our approach. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
18.
韦忠礼 《数学物理学报(B辑英文版)》2014,34(6):1795-1810
We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x(3)(t) + f(t, x(t), x′(t)) = 0, 0 t 1,x(0)-m1∑i=1 αi x(ξi) = 0, x′(0)-m2∑i=1 βi x′(ηi) = 0, x′(1)=0,where 0 ≤ ai≤m1∑i=1 αi 1, i = 1, 2, ···, m1, 0 ξ1 ξ2 ··· ξm1 1, 0 ≤βj≤m2∑i=1βi1,J=1,2, ···, m2, 0 η1 η2 ··· ηm2 1. And we obtain some necessa βi =11, j = 1,ry and sufficient conditions for the existence of C1[0, 1] and C2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f(t, x, y)may be singular at x, y, t = 0 and/or t = 1. 相似文献
19.
讨论边值问题（（一v＇（r））~n）＇=λ（v~α＋v~β）,v＇（0）=v（1）=0,其中λ〉0是正参数.对（n-α）（n-β）〉0的情形得出了正解的存在唯一性.对0〈α〈n〈β的情形得到,存在λ~＊〉0,使得当0〈λ〈λ~＊时,此边值问题恰好存在两个正解;当λ=λ~＊时,此边值问题存在唯一一个正解;当λ〉λ~＊时,此边值问题不存在正解. 相似文献
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We consider Dirichlet boundary value problems for a class of nonlinear ordinary differential equations motivated by the study of radial solutions of equations which are perturbations of the p-Laplacian. 相似文献