共查询到20条相似文献,搜索用时 750 毫秒
1.
We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C1-boundary, the other stated for sets with finite perimeter. 相似文献
2.
C. Palencia 《Numerische Mathematik》1999,82(3):471-490
We consider semidiscretizations in time, based on the backward Euler method, of an abstract, non-autonomous parabolic initial
value problem where , , is a family of sectorial operators in a Banach space X. The domains are allowed to depend on t. Our hypotheses are fulfilled for classical parabolic problems in the , , norms. We prove that the semidiscretization is stable in a suitable sense. We get optimal estimates for the error even when
non-homogeneous boundary values are considered. In particular, the results are applicable to the analysis of the semidiscretizations
of time-dependent parabolic problems under non-homogeneous Neumann boundary conditions.
Received October 17, 1997 / Revised version received April 17, 1998 相似文献
3.
《偏微分方程通讯》2013,38(1-2):175-203
We study the free boundary of solutions to some obstacle problems in the elliptic and parabolic cases. In the one-phase Stefan problem, the parabolic case, we prove that the points where the zero set has no density lie in a Lipschitz surface in space and time. For some fully nonlinear elliptic equations of second order, we get similar results. Furthermore, we prove the C 1 regularity for singular points with some (n ? 1)-dimensional density. 相似文献
4.
Chiranjib Mukherjee 《纯数学与应用数学通讯》2017,70(12):2366-2404
We are interested in the analysis of Gibbs measures defined on two independent Brownian paths in ?d interacting through a mutual self‐attraction. This is expressed by the Hamiltonian with two probability measures μ and ν representing the occupation measures of two independent Brownian motions. We will be interested in a class of potentials V that are singular , e.g., Dirac‐ or Coulomb‐type interactions in ?3, or the correlation function of the parabolic Anderson problem with white noise potential. The mutual interaction of the Brownian paths inspires a compactification of the quotient space of orbits of product measures, which is structurally different from the self‐interacting case introduced in [27], owing to the lack of shift‐invariant structure in the mutual interaction. We prove a strong large‐deviation principle for the product measures of two Brownian occupation measures in such a compactification and derive asymptotic path behavior under Gibbs measures on Wiener paths arising from mutually attracting singular interactions. For the spatially smoothened parabolic Anderson model with white noise potential, our analysis allows a direct computation of the annealed Lyapunov exponents, and a strict ordering of them implies the intermittency effect present in the smoothened model. © 2017 Wiley Periodicals, Inc. 相似文献
5.
We prove that a backward orbit with bounded Kobayashi step for a hyperbolic, parabolic or strongly elliptic holomorphic self-map of a bounded strongly convex C2 domain in Cd necessarily converges to a repelling or parabolic boundary fixed point, generalizing previous results obtained by Poggi-Corradini in the unit disk and by Ostapyuk in the unit ball of Cd. 相似文献
6.
We prove a general convergence result for singular perturbations with an arbitrary number of scales of fully nonlinear degenerate parabolic PDEs. As a special case we cover the iterated homogenization for such equations with oscillating initial data. Explicit examples, among others, are the two-scale homogenization of quasilinear equations driven by a general hypoelliptic operator and the n-scale homogenization of uniformly parabolic fully nonlinear PDEs. 相似文献
7.
V. S. Klimov 《Mathematical Notes》1997,62(4):405-413
We study a regularization method for solving the Cauchy problem for parabolic inclusions that arise in the mechanics of visco-plastic
media. We also consider some applications of the regularization method to the problem of forced oscillations and prove that
the set of solutions to the Cauchy problem is acyclic for the parabolic inclusions under consideration.
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 483–493, October, 1997.
Translated by M. A. Shishkova 相似文献
8.
Jeffrey D. Streets 《Journal of Geometric Analysis》2008,18(1):249-271
We study the gradient flow of the Riemannian functional ℱ(g):=∫
M
|Rm|2. This flow corresponds to a fourth-order degenerate parabolic equation for a Riemannian metric. We prove that the degeneracies
may be accounted for entirely by diffeomorphism flow, and hence we show short-time existence using the DeTurck method. We
prove L
2 derivative estimates of Bernstein-Bando-Shi type and use these to give a basic obstruction to long time existence and prove
a compactness theorem.
相似文献
9.
Farid Ammar-Khodja Assia Benabdallah Cédric Dupaix Manuel González-Burgos 《Journal of Evolution Equations》2009,9(2):267-291
We present a generalization of the Kalman rank condition to the case of n × n linear parabolic systems with constant coefficients and diagonalizable diffusion matrix. To reach the result, we are led
to prove a global Carleman estimate for the solutions of a scalar 2n-order parabolic equation and deduce from it an observability inequality for our adjoint system.
G.-B. Manuel was supported by D.G.E.S. (Spain), grant MTM2006-07932. 相似文献
10.
Potential Analysis - We prove existence of invariant measures for the Markovian semigroup generated by the solution to a parabolic semilinear stochastic PDE whose nonlinear drift term satisfies... 相似文献
11.
N. A. Watson 《Rendiconti del Circolo Matematico di Palermo》1988,37(1):150-160
We study the behaviour of certain hyperplane mean values of solutions of parabolic equations on an infinite strip, and use
our results to prove a representation theorem for solutions which satisfy a one-sidedL
p constraint. 相似文献
12.
We establish the correct solvability (in both directions) of the Cauchy problem for Petrovskii parabolic equations with time-dependent coefficients in S-type spaces. We also prove that a solution of this problem stabilizes to zero in the sense of the topology of these spaces. 相似文献
13.
Feiyue He Anthony Leung Srdjan Stojanovic 《Mathematical Methods in the Applied Sciences》1995,18(2):127-146
This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed. 相似文献
14.
We study the automorphism group of a Cartan geometry, and prove an embedding theorem analogous to a result of Zimmer for automorphism
groups of G-structures. Our embedding theorem leads to general upper bounds on the real rank or nilpotence degree of a Lie subgroup of
the automorphism group. We prove that if the maximal real rank is attained in the automorphism group of a geometry of parabolic
type, then the geometry is flat and complete. 相似文献
15.
Summary
We prove local solvability of quasilinear parabolic systems by means of classical techniques based upon a priori estimates, without assuming any growth condition. 相似文献
16.
Sorin Micu Jaime H. Ortega Ademir F. Pazoto 《Journal of Fourier Analysis and Applications》2011,17(5):991-1007
This article considers a hyperbolic equation perturbed by a vanishing viscosity term depending on a small parameter ε>0. We show that the resulting parabolic equation is null-controllable. Moreover, we provide uniform estimates, with respect
to ε, for the parabolic controls and we prove their convergence to a control of the limit hyperbolic equation. The method we use
is based on Fourier expansion of solutions and the analysis of a biorthogonal sequence to a family of complex exponential
functions. 相似文献
17.
P. Poláčik 《偏微分方程通讯》2013,38(11):1567-1593
We consider quasilinear parabolic equations on ? N satisfying certain symmetry conditions. We prove that bounded positive solutions decaying to zero at spatial infinity are asymptotically radially symmetric about a center. The asymptotic center of symmetry is not fixed a priori (and depends on the solution) but it is independent of time. We also prove a similar theorem on reflectional symmetry. 相似文献
18.
A degenerate parabolic equation modelling the spread of an epidemic 总被引:10,自引:0,他引:10
Maura Ughi 《Annali di Matematica Pura ed Applicata》1986,143(1):385-400
Summary
We consider the Cauchy problem for a degenerate parabolic equation, not in divergence form, representing the diffusive approximation of a model for the spread of an epidemic in a closed population without remotion. We prove existence and uniqueness of the weak solution, defined in a suitable way, and some qualitative properties. 相似文献
19.
Let P be a parabolic subgroup of a complex simple linear algebraic groupG. We prove that the tangent bundle T (G/P) is stable. 相似文献
20.
Dani Szpruch 《Israel Journal of Mathematics》2013,195(2):897-971
Let $\overline {S{p_{2n}}({\rm{<Emphasis FontCategory="NonProportional">F</Emphasis>}})} $ be the metaplectic double cover of F where F is a local field of characteristic 0. We use the Uniqueness of Whittaker model to define a metaplectic analog to Shahidi local coefficients and we use these coefficients to define gamma factors. We show that these gamma factors are multiplicative and satisfy the crude global functional equation. Then, we compute these factors in various cases and obtain explicit formulas for Plancherel measures. These computations are then used to prove some irreducibility theorems for parabolic induction on the metaplectic group over p-adic fields. In particular, we show that all principal series representations induced from unitary characters are irreducible. We also prove that parabolic induction from unitary supercuspidal representation of the Siegel parabolic sub group is irreducible if and only if a certain parabolic induction on F is irreducible. 相似文献