共查询到20条相似文献,搜索用时 15 毫秒
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We propose and study a new variant of the Burgers equation with dissipation fluxes that saturate as the gradients become unbounded. If the upstream-downstream transition is above a critical threshold, the corresponding Riemann problem admits a weak solution wherein part of the transit is accomplished by a jump. It is shown that the solution to a Cauchy problem with sufficiently small compact or periodic initial data preserves its initial smoothness. © 1997 John Wiley & Sons, Inc. 相似文献
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We prove existence and (in some special case) uniqueness of an invariant measure for the transition semigroup associated with the stochastic wave equations with nonlinear dissipative damping. 相似文献
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Jia Yuan 《Journal of Mathematical Analysis and Applications》2008,340(1):334-339
In this paper we consider the 2D dissipative quasi-geostrophic equations and study the regularity criterion of the solutions. By means of a commutator estimate based on frequency localization and Bony's paraproduct decomposition, we obtain a regularity criterion
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A. S. Holevo 《Probability Theory and Related Fields》1996,104(4):483-500
Summary A general existence and uniqueness theorem for solutions of linear dissipative stochastic differential equation in a Hilbert space is proved. The dual equation is introduced and the duality relation is established. Proofs take inspirations from quantum stochastic calculus, however without using it. Solutions of both equations provide classical stochastic representation for a quantum dynamical semigroup, describing quantum Markovian evolution. The problem of the mean-square norm conservation, closely related to the unitality (non-explosion) of the quantum dynamical semigroup, is considered and a hyperdissipativity condition, ensuring such conservation, is discussed. Comments are given on the existence of solutions of a nonlinear stochastic differential equation, introduced and discussed recently in physical literature in connection with continuous quantum measurement processes. 相似文献
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Nicolae H. Pavel 《Israel Journal of Mathematics》1983,46(1-2):103-122
LetX be a real Banach space and letA∶D(A)⊂X→X be the (linear) infinitesimal generator of the semigroupS(t) of classC
0 (of type ω). Assume that the function (t,x)→F(t,x) is continuous, the domainD(t)=D(F(t,·)) is such thatt→D(t) is closed and for eacht∈(a,b), the operatorx→F(t,x) is dissipative. One proves that the subtangential condition (A5) is necessary and sufficient for the existence of the mild
solution to the equationu′=Au+F(t,u). All previous results of this type are included here. An elementary method for proving the uniqueness is pointed out and
applications to PDE are given. 相似文献
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Maisa Khader 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):3945-3963
We study the long time behavior of solutions for damped wave equations with absorption. These equations are generally accepted as models of wave propagation in heterogeneous media with space-time dependent friction a(t,x)ut and nonlinear absorption |u|p−1u (Ikawa (2000) [17]). We consider 1<p<(n+2)/(n−2) and separable a(t,x)=λ(x)η(t) with λ(x)∼(1+|x|)−α and η(t)∼(1+t)−β satisfying conditions (A1) or (A2) which are given. The main results are precise decay estimates for the energy, L2 and Lp+1 norms of solutions. We also observe the following behavior: if α∈[0,1), β∈(−1,1) and 0<α+β<1, there are three different regions for the decay of solutions depending on p; if α∈(−∞,0) and β∈(−1,1), there are only two different regions for the decay of the solutions depending on p. 相似文献
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We study the initial boundary value problem of semilinear hyperbolic equations with dissipative term. By introducing a family of potential wells we derive the invariant sets and vacuum isolating of solutions. Then we prove the global existence, nonexistence and asymptotic behaviour of solutions. In particular we obtain some sharp conditions for global existence and nonexistence of solutions. 相似文献
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In this paper we are interested in the existence of solutions of the following initial value problem: on (0,T) with u(0)=u0 where A:V→V′ is a monotone operator, G:V→V′ is a nonlinear nonmonotone operator and f:(0,T)→V′ is a measurable function, by means of a recent generalization of the famous KKM-Fan’s lemma. 相似文献
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We investigate Lie–Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure. The order of convergence is also investigated in detail, and some numerical illustrations are presented. 相似文献
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Chunyou Sun 《Journal of Differential Equations》2010,248(2):342-362
This paper is devoted to proving some asymptotic regularity, for both reaction-diffusion equation with a polynomially growing nonlinearity of arbitrary order and strongly damped wave equation with critical nonlinearity, which excel the sharp regularity allowed by the corresponding stationary equations (equilibrium points). Based on this regularity, the existence of the finite-dimensional global and exponential attractors can be obtained easily. 相似文献
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Operator splitting methods for a special class of nonlinear partial differential equations with delay are investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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We study a uniform attractor $\mathcal{A}^\varepsilon $ for a dissipative wave equation in a bounded domain Ω ? ?n under the assumption that the external force singularly oscillates in time; more precisely, it is of the form g 0(x, t)+ ε?α g 1 (x, t/ε), x ∈ Ω, t ∈ ?, where α > 0, 0 < ε ≤ 1. In E = H 0 1 × L 2, this equation has an absorbing set B ε estimated as ‖B ε‖ E ≤C 1+C 2ε?α and, therefore, can increase without bound in the norm of E as ε → 0+. Under certain additional constraints on the function g 1(x, z), x ∈ Ω, z ∈ ?, we prove that, for 0 < α ≤ α 0, the global attractors $\mathcal{A}^\varepsilon $ of such an equation are bounded in E, i.e., $\parallel \mathcal{A}^\varepsilon \parallel _E \leqslant C_3 $ , 0 < ε ≤ 1. Along with the original equation, we consider a “limiting” wave equation with external force g 0(x, t) that also has a global attractor $\mathcal{A}^0 $ . For the case in which g 0(x, t) = g 0(x) and the global attractor $\mathcal{A}^0 $ of the limiting equation is exponential, it is established that, for 0 < α ≤ α 0, the Hausdorff distance satisfies the estimate $dist_E (\mathcal{A}^\varepsilon ,\mathcal{A}^0 ) \leqslant C\varepsilon ^{\eta (\alpha )} $ , where η(α) > 0. For η(α) and α 0, explicit formulas are given. We also study the nonautonomous case in which g 0 = g 0(x, t). It is assumed that sufficient conditions are satisfied for which the “limiting” nonautonomous equation has an exponential global attractor. In this case, we obtain upper bounds for the Hausdorff distance of the attractors $\mathcal{A}^\varepsilon $ from $\mathcal{A}^0 $ , similar to those given above. 相似文献
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HUANG Jian-hua 《高校应用数学学报(A辑)》2012,27(1)
利用修正的Lyapunov-Perron方法研究随机耗散时滞波方程不变流形的存在性,证明了当谱间隙条件成立和时滞适当小时,随机耗散时滞波方程存在随机惯性流形,并且谱间隙条件与确定型时滞耗散波方程的一致. 相似文献
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Mitsuhiro Nakao 《Journal of Differential Equations》2006,227(1):204-229
We show the existence, size and some absorbing properties of global attractors of the nonlinear wave equations with nonlinear dissipations like ρ(x,ut)=a(x)r|ut|ut. 相似文献
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The Cauchy-Goursat problem for wave equations with nonlinear dissipative term is studied. The existence, uniqueness, and blow-up of global solutions of this problem are considered. The local solvability of this problem is also discussed. 相似文献