共查询到20条相似文献,搜索用时 15 毫秒
1.
N. V. Krylov 《偏微分方程通讯》2016,41(4):644-664
Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of (t, x) bounded away from 0. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations. 相似文献
2.
Shuxuan Li 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3716-3727
In this paper, taking the Hessian Sobolev inequality (0<p≤k) (X.-J. Wang, 1994 [2]) as the starting point, we give a proof of the Hessian Sobolev inequality when k<p≤k∗, where k∗ is the critical Sobolev embedding index of k-Hessian type. We also prove that k∗ is optimal by one-dimensional Hardy’s inequality. 相似文献
3.
4.
G. V. Demidenko 《Siberian Mathematical Journal》2008,49(5):842-851
We consider a class of matrix quasielliptic operators on the n-dimensional space. For these operators, we establish the isomorphism properties in some special scales of weighted Sobolev spaces. Basing on these properties, we prove the unique solvability of the initial value problem for a class of Sobolev type equations. 相似文献
5.
R. Quintanilla 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):595-603
In this note we investigate the spatial behavior of several nonlinear parabolic equations with nonlinear boundary conditions.
Under suitable conditions on the nonlinear terms we prove that the solutions either cease to exist for a finite value of the
spatial variable or else they decay algebraically. The main tool used is the weighted energy method. Our results can be applied
to several situations concerning heat conduction.
Received: April 4, 2004; revised: September 20, 2004 相似文献
6.
A. Fiorenza
A. Mercaldo
J. M. Rakotoson
《Applied Mathematics Letters》2001,14(8):979-981We extend the results of [1–5] on the uniqueness of solutions of parabolic equations. Our results give also some regularity results which complete the existence results made in [6–8]. 相似文献
7.
The aim of this paper is to establish some logarithmically improved regularity criteria in term of the multiplier spaces to the Navier-Stokes equations. 相似文献
8.
Alejandro Velez Santiago 《Journal of Mathematical Analysis and Applications》2010,372(1):120-698
Let p∈(1,N), Ω⊂RN a bounded W1,p-extension domain and let μ be an upper d-Ahlfors measure on ∂Ω with d∈(N−p,N). We show in the first part that for every p∈[2N/(N+2),N)∩(1,N), a realization of the p-Laplace operator with (nonlinear) generalized nonlocal Robin boundary conditions generates a (nonlinear) strongly continuous submarkovian semigroup on L2(Ω), and hence, the associated first order Cauchy problem is well posed on Lq(Ω) for every q∈[1,∞). In the second part we investigate existence, uniqueness and regularity of weak solutions to the associated quasi-linear elliptic equation. More precisely, global a priori estimates of weak solutions are obtained. 相似文献
9.
We consider the regularity problem for 3D Navier-Stokes equations in a bounded domain with smooth boundary. A new sufficient condition which guarantees the regularity of weak solutions on the quotient ∇p/(1+|u|δ1+|∇u|δ2) for the Navier-Stokes equations is established. 相似文献
10.
11.
Ahmed Alsaedi Mohammed S. Alhothuali Bashir Ahmad Sebti Kerbal Mokhtar Kirane 《Mathematical Methods in the Applied Sciences》2014,37(13):2009-2016
Sobolev type nonlinear equations with time fractional derivatives are considered. Using the test function method, limiting exponents for nonexistence of solutions are found. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
12.
Hongjie Dong Hong Zhang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(4):971-992
We obtain Dini type estimates for a class of concave fully nonlinear nonlocal elliptic equations of order with rough and non-symmetric kernels. The proof is based on a novel application of Campanato's approach and a refined estimate in [9]. 相似文献
13.
A Discontinuous Galerkin method with interior penalties is presented for nonlinear Sobolev equations. A semi‐discrete and a family of fully‐discrete time approximate schemes are formulated. These schemes are symmetric. Hp‐version error estimates are analyzed for these schemes. For the semi‐discrete time scheme a priori L∞(H1) error estimate is derived and similarly, l∞(H1) and l2(H1) for the fully‐discrete time schemes. These results indicate that spatial rates in H1 and time truncation errors in L2 are optimal. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
14.
A discontinuous Galerkin method with interior penalties is presented for nonlinear Sobolev equations. A semi-discrete and a family of Fully-discrete time approximate scheme are formulated. These schemes can be symmetric or nonsymmetric. Hp-version error estimates are analyzed for these schemes. Just because of a damping term ·(b(u)ut) included in Sobolev equation, which is the distinct character different from parabolic equation, special test functions are chosen to deal with this term. Finally, a priori L∞(H1) error estimate is derived for the semi-discrete time scheme and similarly, l∞(H1) and l2(H1) for the Fully-discrete time schemes. These results also indicate that spatial rates in H1 and time truncation errors in L2 are optimal. 相似文献
15.
16.
In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi [H. Kozono, Y. Taniuchi, Limiting case of the Sobolev inequality in BMO, with application to the Euler equations, Comm. Math. Phys. 214 (2000) 191-200] have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) BMO norm. In this paper, we show a parabolic version of the Kozono-Taniuchi inequality by means of anisotropic (parabolic) BMO norm. More precisely we give an upper bound for the L∞ norm of a function in terms of its parabolic BMO norm, up to a logarithmic correction involving its norm in some Sobolev space. As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems. 相似文献
17.
The paper studies stochastic partial differential equations of parabolic type with Dirichlet boundary conditions. Solvability, uniqueness, and a priori estimates similar to the second fundamental inequality are obtained for bounded and unbounded domains. For the case of discontinuous coefficients, some Cordes type conditions that ensure solvability are suggested. 相似文献
18.
19.
E. Grenier 《Journal de Mathématiques Pures et Appliquées》1997,76(10):965-990
In this paper we study boundary layers of nonlinear characteristic parabolic equations as the viscosity goes to zero. We obtain and justify in small time a complete expansion of the solution with respect to the viscosity. 相似文献
20.
Philip W. Schaefer 《Expositiones Mathematicae》2006,24(4):371-377
A priori bounds are determined for certain energy expressions for a class of semi-linear parabolic and hyperbolic initial-boundary value problems when a combination of the values of the solution initially and at a later time is prescribed. 相似文献