共查询到20条相似文献,搜索用时 31 毫秒
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We are concerned with entropy solutions of the 2×2 relativistic Euler equations for perfect fluids in special relativity. We establish the uniqueness of Riemann solutions in the class of entropy solutions in L∞∩BVloc with arbitrarily large oscillation. Our proof for solutions with large oscillation is based on a detailed analysis of global behavior of shock curves in the phase space and on special features of centered rarefaction waves in the physical plane for this system. The uniqueness result does not require specific reference to any particular method for constructing the entropy solutions. Then the uniqueness of Riemann solutions yields their inviscid large-time stability under arbitrarily largeL1∩L∞∩BVloc perturbation of the Riemann initial data, as long as the corresponding solutions are in L∞ and have local bounded total variation that allows the linear growth in time. We also extend our approach to deal with the uniqueness and stability of Riemann solutions containing vacuum in the class of entropy solutions in L∞ with arbitrarily large oscillation. 相似文献
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Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2007,211(3):609-621
Let (X,L) be a polarized manifold of dimension n defined over the field of complex numbers. In this paper, we treat the case where n=3 and 4. First we study the case of n=3 and we give an explicit lower bound for h0(KX+L) if κ(X)≥0. Moreover, we show the following: if κ(KX+L)≥0, then h0(KX+L)>0 unless κ(X)=−∞ and h1(OX)=0. This gives us a partial answer of Effective Non-vanishing Conjecture for polarized 3-folds. Next for n=4 we investigate the dimension of H0(KX+mL) for m≥2. If n=4 and κ(X)≥0, then a lower bound for h0(KX+mL) is obtained. We also consider a conjecture of Beltrametti-Sommese for 4-folds and we can prove that this conjecture is true unless κ(X)=−∞ and h1(OX)=0. Furthermore we prove the following: if (X,L) is a polarized 4-fold with κ(X)≥0 and h1(OX)>0, then h0(KX+L)>0. 相似文献
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M. Perović 《Commentarii Mathematici Helvetici》1986,61(1):60-66
A homeomorphismf:B
n→B
n of the unit ball inR
n(n≥2) whose coefficient of quasiconformality in the ball of radiusr<1 has asymptotic rate of growthK(r)=sup
|x|≤r
k(x, f)=O(log (1/1−r)) can be continued to a homeomorphism
of the closed ball
. Forn=2 this implies that the Caratheodory theory of prime ends for conformal mappings also holds for the class of homeomorphismsf:B
2→D withK(r)=O(log (1/1−r)).
This work was partially supported by SIZ za nauku SRCG, Titograd. 相似文献
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Lu Yang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):3876-3883
In this paper, we study the long-time behavior of the reaction-diffusion equation with dynamical boundary condition, where the nonlinear terms f and g satisfy the polynomial growth condition of arbitrary order. Some asymptotic regularity of the solution has been proved. As an application of the asymptotic regularity results, we can not only obtain the existence of a global attractor A in (H1(Ω)∩Lp(Ω))×Lq(Γ) immediately, but also can show further that A attracts every L2(Ω)×L2(Γ)-bounded subset with (H1(Ω)∩Lp+δ(Ω))×Lq+κ(Γ)-norm for any δ,κ∈[0,∞). 相似文献
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Tomasz Piasecki 《Journal of Differential Equations》2010,248(8):2171-2198
We investigate a steady flow of a viscous compressible fluid with inflow boundary condition on the density and inhomogeneous slip boundary conditions on the velocity in a cylindrical domain Ω=Ω0×(0,L)∈R3. We show existence of a solution , p>3, where v is the velocity of the fluid and ρ is the density, that is a small perturbation of a constant flow (, ). We also show that this solution is unique in a class of small perturbations of . The term u⋅∇w in the continuity equation makes it impossible to show the existence applying directly a fixed point method. Thus in order to show existence of the solution we construct a sequence (vn,ρn) that is bounded in and satisfies the Cauchy condition in a larger space L∞(0,L;L2(Ω0)) what enables us to deduce that the weak limit of a subsequence of (vn,ρn) is in fact a strong solution to our problem. 相似文献
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Piotr Kot 《Israel Journal of Mathematics》2018,225(2):771-796
We investigate the unbalanced ordinary partition relations of the form λ → (λ, α)2 for various values of the cardinal λ and the ordinal α. For example, we show that for every infinite cardinal κ, the existence of a κ+-Suslin tree implies κ+ ? (κ+, log κ (κ+) + 2)2. The consistency of the positive partition relation b → (b, α)2 for all α < ω1 for the bounding number b is also established from large cardinals. 相似文献
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Reinhard Farwig Hermann Sohr 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1459-1465
There are only very few results on the existence of unique local in time strong solutions of the Navier-Stokes equations for completely general domains Ω⊆R3, although domains with edges and corners, bounded or unbounded, are very important in applications. The reason is that the Lq-theory for the Stokes operator A is available in general only in the Hilbert space setting, i.e., with q=2. Our main result for a general domain Ω is optimal in a certain sense: Consider an initial value and a zero external force. Then the condition is sufficient and necessary for the existence of a unique local strong solution u∈L8(0,T;L4(Ω)) in some interval [0,T), 0<T≤∞, with u(0)=u0, satisfying Serrin’s condition . Note that Fujita-Kato’s sufficient condition u0∈D(A1/4) is strictly stronger and therefore not optimal. 相似文献
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Xin ZhongXing-Ping Wu Chun-Lei Tang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3829-3848
We introduce Triebel-Lizorkin-Lorentz function spaces, based on the Lorentz Lp,q-spaces instead of the standard Lp-spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations of inviscid incompressible fluid in Rn,n≥2. As a corollary we obtain global existence of solutions to the 2D Euler equations in the Triebel-Lizorkin-Lorentz space. For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator estimates in our spaces. The key methods of proof used are the Littlewood-Paley decomposition and the paradifferential calculus by J.M. Bony. 相似文献
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Octavian G. Mustafa 《Journal of Mathematical Analysis and Applications》2008,348(1):211-219
We give a constructive proof of existence to oscillatory solutions for the differential equations x″(t)+a(t)λ|x(t)|sign[x(t)]=e(t), where t?t0?1 and λ>1, that decay to 0 when t→+∞ as O(t−μ) for μ>0 as close as desired to the “critical quantity” . For this class of equations, we have limt→+∞E(t)=0, where E(t)<0 and E″(t)=e(t) throughout [t0,+∞). We also establish that for any μ>μ? and any negative-valued E(t)=o(t−μ) as t→+∞ the differential equation has a negative-valued solution decaying to 0 at + ∞ as o(t−μ). In this way, we are not in the reach of any of the developments from the recent paper [C.H. Ou, J.S.W. Wong, Forced oscillation of nth-order functional differential equations, J. Math. Anal. Appl. 262 (2001) 722-732]. 相似文献
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Peter Giesl 《Journal of Mathematical Analysis and Applications》2007,335(1):461-479
We consider the general nonlinear differential equation with x∈R2 and develop a method to determine the basin of attraction of a periodic orbit. Borg's criterion provides a method to prove existence, uniqueness and exponential stability of a periodic orbit and to determine a subset of its basin of attraction. In order to use the criterion one has to find a function W∈C1(R2,R) such that LW(x)=W′(x)+L(x) is negative for all x∈K, where K is a positively invariant set. Here, L(x) is a given function and W′(x) denotes the orbital derivative of W. In this paper we prove the existence and smoothness of a function W such that LW(x)=−μ‖f(x)‖. We approximate the function W, which satisfies the linear partial differential equation W′(x)=〈∇W(x),f(x)〉=−μ‖f(x)‖−L(x), using radial basis functions and obtain an approximation w such that Lw(x)<0. Using radial basis functions again, we determine a positively invariant set K so that we can apply Borg's criterion. As an example we apply the method to the Van-der-Pol equation. 相似文献
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Matthew Boylan 《Journal of Number Theory》2003,98(2):377-389
Let F(z)=∑n=1∞a(n)qn denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that
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Antonio Russo 《Journal of Differential Equations》2011,251(9):2387-2408
The Navier problem is to find a solution of the steady-state Navier-Stokes equations such that the normal component of the velocity and a linear combination of the tangential components of the velocity and the traction assume prescribed value a and s at the boundary. If Ω is exterior it is required that the velocity converges to an assigned constant vector u0 at infinity. We prove that a solution exists in a bounded domain provided ‖a‖L2(∂Ω) is less than a computable positive constant and is unique if ‖a‖W1/2,2(∂Ω)+‖s‖L2(∂Ω) is suitably small. As far as exterior domains are concerned, we show that a solution exists if ‖a‖L2(∂Ω)+‖a−u0⋅n‖L2(∂Ω) is small. 相似文献
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Gordon Blower 《Journal of Mathematical Analysis and Applications》2009,355(1):311-316
In random matrix theory, determinantal random point fields describe the distribution of eigenvalues of self-adjoint matrices from the generalized unitary ensemble. This paper considers symmetric Hamiltonian systems and determines the properties of kernels and associated determinantal random point fields that arise from them; this extends work of Tracy and Widom. The inverse spectral problem for self-adjoint Hankel operators gives sufficient conditions for a self-adjoint operator to be the Hankel operator on L2(0,∞) from a linear system in continuous time; thus this paper expresses certain kernels as squares of Hankel operators. For suitable linear systems (−A,B,C) with one-dimensional input and output spaces, there exists a Hankel operator Γ with kernel ?(x)(s+t)=Ce−(2x+s+t)AB such that gx(z)=det(I+(z−1)ΓΓ†) is the generating function of a determinantal random point field on (0,∞). The inverse scattering transform for the Zakharov-Shabat system involves a Gelfand-Levitan integral equation such that the trace of the diagonal of the solution gives . When A?0 is a finite matrix and B=C†, there exists a determinantal random point field such that the largest point has a generalised logistic distribution. 相似文献
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Let O ? R d be a bounded domain of class C 1,1. Let 0 < ε - 1. In L 2(O;C n ) we consider a positive definite strongly elliptic second-order operator B D,ε with Dirichlet boundary condition. Its coefficients are periodic and depend on x/ε. The principal part of the operator is given in factorized form, and the operator has lower order terms. We study the behavior of the generalized resolvent (B D,ε ? ζQ 0(·/ε))?1 as ε → 0. Here the matrix-valued function Q 0 is periodic, bounded, and positive definite; ζ is a complex-valued parameter. We find approximations of the generalized resolvent in the L 2(O;C n )-operator norm and in the norm of operators acting from L 2(O;C n ) to the Sobolev space H 1(O;C n ) with two-parameter error estimates (depending on ε and ζ). Approximations of the generalized resolvent are applied to the homogenization of the solution of the first initial-boundary value problem for the parabolic equation Q 0(x/ε)? t v ε (x, t) = ?(B D,ε v ε )(x, t). 相似文献
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Margarita Ramalho 《Algebra Universalis》1985,20(2):243-253
For a pseudocomplemented latticeL, we prove that the filter Dn(L), 1n<, generated by then-strongly dense elements is contained in everyn-normal filter. Hence, Dn(L)=Gn(L)=Radn (L), where Gn(L) is the intersection of all n-normal filters, and Radn (L) is the intersection of alln-normal prime filters. Moreover, we prove that a prime filterP is n-normal iff Dn(L)=P. Consequently, for
, we have Dn(L)=Gn(L)=Radn (L) and therefore
iff Radn(L)={1} (or iff Gn(L)={1}).Considering the skeleton S(L) ofL, a complete clarification of the relationship between filters ofL and S(L) is given by studying th correspondence FFS(L).We state that D(L) (and that D1(L), if
is an irredundant intersection of maximal filters (resp. of *-maximal filters) iff S(L) is finite.Finally, for
we state that the least *-congruence for which
is that one generated by Dn(L).Presented by B. Jónsson.Research supported by the I.N.I:C, (Centro de Algebra da Universidade de Lisboa). 相似文献
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Xiaofei Song 《Linear algebra and its applications》2008,429(7):1579-1586
Let Mn be the algebra of all n×n complex matrices and Γn the set of all k-potent matrices in Mn. Suppose ?:Mn→Mn is a map satisfying A-λB∈Γn implies ?(A)-λ?(B)∈Γn, where A, B∈Mn, λ∈C. Then either ? is of the form ?(A)=cTAT-1, A∈Mn, or ? is of the form ?(A)=cTAtT-1, A∈Mn, where T∈Mn is an invertible matrix, c∈C satisfies ck=c. 相似文献
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The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2?) with respect to non-homogeneous term g(x) ∈ L 2 n/2 (B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H 2,0 1,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem. 相似文献