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31.
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A macroscopic model for an intermediate state between type‐I and type‐II superconductivity 下载免费PDF全文
Karel Van Bockstal Marián Slodička 《Numerical Methods for Partial Differential Equations》2015,31(5):1551-1567
A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type‐I and type‐II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen's model. The nonlinearity is coming from the power law relation by Rhyner. The well‐posedness of the problem is discussed under low regularity assumptions and the error estimate for a semi‐implicit time‐discrete scheme based on backward Euler approximation is established. In the proofs, the monotonicity methods and the Minty–Browder argument are used. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1551–1567, 2015 相似文献
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In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, the same Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for Riemannian metrics proved by Burq-Gérard-Tzvetkov to the non-elliptic case and improves the result by Salort for the degenerate case. We also investigate the optimality of the result for the case on 𝕊3 × 𝕊3. 相似文献
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Yongtao LIU 《Frontiers of Mathematics in China》2021,16(3):783
By using the perpetual cutoff method, we prove two discrete versions of gradient estimates for bounded Laplacian on locally finite graphs with exception sets under the condition of (K,N). This generalizes a main result of F. Münch who considers the case of CD(K, ) curvature. Hence, we answer a question raised by Münch. For that purpose, we characterize some basic properties of radical form of the perpetual cutoff semigroup and give a weak commutation relation between bounded Laplacian and perpetual cutoff semigroup in our setting. 相似文献
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Lutz Angermann 《Numerical Methods for Partial Differential Equations》2002,18(2):241-259
This article investigates Petrov‐Galerkin discretizations of operator equations with linearly stable operators, where the residual does not belong to the annihilator W of the discrete test space Wh. Conforming and nonconforming methods are considered separately, and for the treatment of the nonconforming situation the concept of elliptic lifting is introduced. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 241–259, 2002; DOI 10.1002/num.1005 相似文献
39.
Tadeusz Iwaniec 《Transactions of the American Mathematical Society》2002,354(5):1961-1995
This paper has arisen from an effort to provide a comprehensive and unifying development of the -theory of quasiconformal mappings in . The governing equations for these mappings form nonlinear differential systems of the first order, analogous in many respects to the Cauchy-Riemann equations in the complex plane. This approach demands that one must work out certain variational integrals involving the Jacobian determinant. Guided by such integrals, we introduce two nonlinear differential operators, denoted by and , which act on weakly differentiable deformations of a domain .
Solutions to the so-called Cauchy-Riemann equations and are simply conformal deformations preserving and reversing orientation, respectively. These operators, though genuinely nonlinear, possess the important feature of being rank-one convex. Among the many desirable properties, we give the fundamental -estimate
In quest of the best constant , we are faced with fascinating problems regarding quasiconvexity of some related variational functionals. Applications to quasiconformal mappings are indicated.
40.
Lech Zielinski 《Mathematical Physics, Analysis and Geometry》1999,2(3):291-321
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients. 相似文献