共查询到20条相似文献，搜索用时 15 毫秒
1.
Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Enrico Obrecht Silvia Romanelli 《Mathematische Nachrichten》2010,283(4):504-521
We prove a very general form of the Angle Concavity Theorem, which says that if (T (t)) defines a one parameter semigroup acting over various Lp spaces (over a fixed measure space), which is analytic in a sector of opening angle θp, then the maximal choice for θp is a concave function of 1 – 1/p. This and related results are applied to give improved estimates on the optimal Lp angle of ellipticity for a parabolic equation of the form ?u /?t = Au, where A is a uniformly elliptic second order partial differential operator with Wentzell or dynamic boundary conditions. Similar results are obtained for the higher order equation ?u /?t = (–1)m +lAmu, for all positive integers m. 相似文献
2.
Motivated by a neurobiological problem, we discuss a class of diffusion problems on a network. The celebrated Rall lumped soma model for the spread of electrical potential in a dendritical tree prescribes that the common cable equation must be coupled with particular dynamic conditions in some nodes (the cell bodies, or somata). We discuss the extension of this model to the case of a whole network of neurons, where the ramification nodes can be either active (with excitatory time‐dependent boundary conditions) or passive (where no dynamics take place, i.e. only Kirchhoff laws are imposed). While well‐posedness of the system has already been obtained in previous works, using abstract tools based on variational methods and semigroup theory we are able to prove several qualitative properties, including asymptotic behaviour, regularity of solutions, and monotonicity of the semigroups in dependence on the physical coefficients. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
3.
J. L. Menaldi 《Journal of Optimization Theory and Applications》1982,36(4):535-563
A stopping time problem for degenerate reflected diffusions is studied in this paper. We give a characterization of the optimal cost as the maximum solution of a degenerate elliptic variational inequality with Neumann boundary conditions.The author would like to thank Professor L. C. Evans for very helpful suggestions on this topic. 相似文献
4.
Albo Carlos Cavalheiro 《Applications of Mathematics》2006,51(6):619-628
In the paper we study the equation L
u
= f, where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set μ. We prove existence and uniqueness
of solutions in the space H(μ) for the Neumann problem. 相似文献
5.
In this paper we give necessary and sufficient conditions for the existence of a C>
0-semigroup in L
1(I) (I real interval) generated by a second-order differential operator when suitable boundary conditions at the endpoints are imposed. 相似文献
6.
Giuseppe Maria Coclite Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Silvia Romanelli 《Semigroup Forum》2008,77(1):101-108
The solution u of the well-posed problem
depends continuously on (a
ij
,β,γ,q).
Dedicated to Karl H. Hofmann on his 75th birthday. 相似文献
7.
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
8.
9.
Delio Mugnolo 《Mathematische Nachrichten》2006,279(3):299-318
We define an abstract setting to treat wave equations equipped with time‐dependent acoustic boundary conditions on bounded domains of R n . We prove a well‐posedness result and develop a spectral theory which also allows to prove a conjecture proposed in [13]. Concrete problems are also discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Ciprian G. Gal 《Mathematical Methods in the Applied Sciences》2006,29(17):2009-2036
In this article, we propose a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions are derived from a mass conservation law and variational methods. Employing classical methods, that is, fixed point theorems and standard energy methods, we obtain the existence and uniqueness of a global solution to our problem. We then also compare our model of phase separation with other previous Cahn–Hilliard equations with homogeneous Neumann and dynamic boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
11.
12.
This paper concerns the asymptotics of the linear wave equation with frictional damping only on Wentzell boundary in the square. After reformulating the model into an abstract Cauchy problem, we show that the spectrum for the corresponding operator matrix has no purely imaginary values. Moreover, by analyzing a family of eigenvalues for the operator matrix, we prove that there exists a solution of the system, whose energy decay rate can be arbitrarily slow. 相似文献
13.
In this paper, the authors study the asymptotically linear elliptic equation on manifold with conical singularities ??Bu + λu = a(z)f(u), u ≥ 0 in RN+,where N = n + 1 ≥ 3, λ > 0, z = t,x1,· · · ,xn, and ?B = (t?t)2 + ?2x1 + · · · + ?2xn. Combining properties of cone-degenerate operator, the Pohozaev manifold and qualitative properties of the ground state solution for the limit equation, we obtain a positive solution under some suitable conditions on a and f. 相似文献
14.
M. Bogoya R. Ferreira J.D. Rossi 《Journal of Mathematical Analysis and Applications》2008,337(2):1284-1294
We deal with boundary value problems (prescribing Dirichlet or Neumann boundary conditions) for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation. First, we prove existence, uniqueness and the validity of a comparison principle for these problems. Next, we impose boundary data that blow up in finite time and study the behavior of the solutions. 相似文献
15.
Mahamadi Warma 《Journal of Mathematical Analysis and Applications》2007,336(2):1132-1148
Let Ω⊂RN be a bounded domain with Lipschitz boundary, with a>0 on . Let σ be the restriction to ∂Ω of the (N−1)-dimensional Hausdorff measure and let be σ-measurable in the first variable and assume that for σ-a.e. x∈∂Ω, B(x,⋅) is a proper, convex, lower semicontinuous functional. We prove in the first part that for every p∈(1,∞), the operator Ap:=div(a|∇u|p−2∇u) with nonlinear Wentzell-Robin type boundary conditions
16.
《Integral Transforms and Special Functions》2012,23(6):471-490
A distributional theory of fractional transformations is developed. A constructive approach, based on the eigenfunction expansion method pioneered by Zemanian, is used to produce an appropriate space of test functions and corresponding space of generalized functions. The fractional transformations that are defined are shown to form an equicontinuous group of operators on the space of test functions and a weak* continuous group on the space of generalized functions. Integral representations for the fractional transformations are also obtained under certain conditions. The fractional Fourier transformation is considered as a particular case of our general theory. 相似文献
17.
18.
19.
利用临界点理论中的山路引理,证明一类含退化椭圆算子的Kirchhoff型方程在适当的假设条件下解的存在性,所得结论丰富和发展了已有文献的相关结果. 相似文献