共查询到20条相似文献,搜索用时 31 毫秒
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Yi Zhou 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1543-1561
In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in the first quadrant . Under the assumptions that the system is strictly hyperbolic and linearly degenerate or weakly linearly degenerate, the global existence and uniqueness of C1 solutions are obtained for small initial and boundary data. We also present two applications for physical models. 相似文献
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Lisa Beck 《Journal of Mathematical Analysis and Applications》2009,354(1):301-318
We consider weak solutions of second order nonlinear elliptic systems in divergence form under standard subquadratic growth conditions with boundary data of class C1. In dimensions n∈{2,3} we prove that u is locally Hölder continuous for every exponent outside a singular set of Hausdorff dimension less than n−p. This result holds up to the boundary both for non-degenerate and degenerate systems. In the proof we apply the direct method and classical Morrey-type estimates introduced by Campanato. 相似文献
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We present some new regularity criteria for “suitable weak solutions” of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are Hölder continuous up to the boundary provided that the scaled mixed norm with 3/p+2/q?2, 2<q?∞, (p,q)≠(3/2,∞) is small near the boundary. Our methods yield new results in the interior case as well. Partial regularity of weak solutions is also analyzed under some additional integral conditions. 相似文献
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Roberta Filippucci Marco Rigoli 《Journal of Mathematical Analysis and Applications》2009,356(2):689-2670
In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form , under the main request that h and are continuous on R+. We achieve our conclusions introducing a generalized version of the well-known Keller-Osserman condition. 相似文献
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Zaihong Wang Jing Xia Dongyun Zheng 《Journal of Mathematical Analysis and Applications》2006,321(1):273-285
In this paper, we deal with the existence of periodic solutions of the second order differential equations x″+g(x)=p(t) with singularity. We prove that the given equation has at least one periodic solution when g(x) has singularity at origin, satisfies
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Regularity criterion of axisymmetric weak solutions to the 3D Navier-Stokes equations 总被引:1,自引:0,他引:1
Qionglei Chen 《Journal of Mathematical Analysis and Applications》2007,331(2):1384-1395
We consider the regularity of axisymmetric weak solutions to the Navier-Stokes equations in R3. Let u be an axisymmetric weak solution in R3×(0,T), w=curlu, and wθ be the azimuthal component of w in the cylindrical coordinates. Chae-Lee [D. Chae, J. Lee, On the regularity of axisymmetric solutions of the Navier-Stokes equations, Math. Z. 239 (2002) 645-671] proved the regularity of weak solutions under the condition wθ∈Lq(0,T;Lr), with , . We deal with the marginal case r=∞ which they excluded. It is proved that u becomes a regular solution if . 相似文献
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Let Ω be a bounded domain in RN, N?2, with smooth boundary ∂Ω. We construct positive weak solutions of the problem Δu+up=0 in Ω, which vanish in a suitable trace sense on ∂Ω, but which are singular at prescribed isolated points if p is equal or slightly above . Similar constructions are carried out for solutions which are singular at any given embedded submanifold of ∂Ω of dimension k∈[0,N−2], if p equals or it is slightly above , and even on countable families of these objects, dense on a given closed set. The role of the exponent (first discovered by Brezis and Turner [H. Brezis, R. Turner, On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977) 601-614]) for boundary regularity, parallels that of for interior singularities. 相似文献
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Claudianor O. Alves Marcelo Montenegro 《Journal of Mathematical Analysis and Applications》2009,352(1):112-119
We show the existence of positive solution for the following class of singular Neumann problem in BR with ∂u/∂ν=0 on ∂BR, where R>0, λ>0 is a positive parameter, β>0, p∈[0,1), BR=BR(0)⊂RN, and are radially symmetric nonnegative C1 functions. Using variational methods and sub- and supersolutions, we obtain a solution for an approximated problem involving mixed boundary conditions. The limit of the approximated solutions, is a positive solution. 相似文献
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Large solutions of semilinear elliptic equations under the Keller-Osserman condition 总被引:1,自引:0,他引:1
Alan V. Lair 《Journal of Mathematical Analysis and Applications》2007,328(2):1247-1254
We consider the equation Δu=p(x)f(u) where p is a nonnegative nontrivial continuous function and f is continuous and nondecreasing on [0,∞), satisfies f(0)=0, f(s)>0 for s>0 and the Keller-Osserman condition where . We establish conditions on the function p that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of the given equation. 相似文献
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Ta-Tsien Li Zhi-Qiang Shao De-Xing Kong 《Journal of Mathematical Analysis and Applications》2007,325(1):205-225
It is proven that if the leftmost eigenvalue is weakly linearly degenerate, then the Cauchy problem for a class of nonhomogeneous quasilinear hyperbolic systems with small and decaying initial data given on a semi-bounded axis admits a unique global C1 solution on the domain , where x=xn(t) is the fastest forward characteristic emanating from the origin. As an application of our result, we prove the existence of global classical, C1 solutions of the flow equations of a model class of fluids with viscosity induced by fading memory with small smooth initial data given on a semi-bounded axis. 相似文献
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We present new interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations in dimension three: a suitable weak solution is regular near an interior point z if the scaled -norm of the velocity with 1?3/p+2/q?2, 1?q?∞ is sufficiently small near z and if the scaled -norm of the magnetic field with 1?3/l+2/m?2, 1?m?∞ is bounded near z. Similar results are also obtained for the vorticity and for the gradient of the vorticity. Furthermore, with the aid of the regularity criteria, we exhibit some regularity conditions involving pressure for weak solutions of the magnetohydrodynamic equations. 相似文献
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Lamia Bel Kenani Toukabri 《Journal of Mathematical Analysis and Applications》2010,363(2):596-605
We consider the Monge-Ampère equation det(D2u)=Ψ(x,u,Du) in Rn, n?3, where Ψ is a positive function in C2(Rn×R×Rn). We prove the existence of convex solutions, provided there exist a subsolution of the form and a superharmonic bounded positive function φ satisfying: . 相似文献
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In this paper, we consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in RN, N?4, , is the critical Sobolev exponent, K(x) is a continuous function. When Ω and K(x) are invariant under a group of orthogonal transformations, we prove the existence of nodal and positive solutions for 0<λ<λ1, where λ1 is the first Dirichlet eigenvalue of on Ω. 相似文献
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Positive periodic solutions of functional differential equations 总被引:1,自引:0,他引:1
Haiyan Wang 《Journal of Differential Equations》2004,202(2):354-366
We consider the existence, multiplicity and nonexistence of positive ω-periodic solutions for the periodic equation x′(t)=a(t)g(x)x(t)−λb(t)f(x(t−τ(t))), where are ω-periodic, , , f,g∈C([0,∞),[0,∞)), and f(u)>0 for u>0, g(x) is bounded, τ(t) is a continuous ω-periodic function. Define , , i0=number of zeros in the set and i∞=number of infinities in the set . We show that the equation has i0 or i∞ positive ω-periodic solution(s) for sufficiently large or small λ>0, respectively. 相似文献