共查询到20条相似文献，搜索用时 15 毫秒
1.
Xiaoli Zhu Fuyi Li Zhanping Liang Ting Rong 《Mathematical Methods in the Applied Sciences》2016,39(13):3591-3606
A sufficient condition for blowup of solutions to a class of pseudo‐parabolic equations with a nonlocal term is established in this paper. In virtue of the potential wells method, we first extend the results obtained by Xu and Su in [J. Funct. Anal., 264 (12): 2732‐2763, 2013] to the nonlocal case and describe successfully the behavior of solutions by using the energy functional, Nehari functional, and the ground state energy of the stationary equation. Sequently, we study the boundedness and convergency of any global solution. Finally, we achieve a criterion to guarantee the blowup of solutions without any limit of the initial energy.Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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本文研究了广义两分量Dullin-Gottwald-Holm (GDGH2)浅水波系统及其推广形式的一类自相似解.首先通过构造Emden方程,分析了解的全局存在性,以及在一定条件下解的爆破现象;其次利用扰动方法和特征线法,构造了两种形式的精确解. 相似文献
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Si Xin 《偏微分方程(英文版)》2008,21(4):377-383
Existence and extinction in finite time of global weak solutions for the problem （P） are proved. 相似文献
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ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionInthispaper,weconsiderthefollowinginitial--boundaryvalueproblemwhereQ~fix(o,co),aQ=aflx(o,co),fiisaboundeddomaininEuclideanspaceR"(n22)withsmoothboundaryonandac=(u.,,'Iu..)denotesthegradientoffunctionu(x).Weassumethefunctionsal(x,t,u,p)(i=1,2,',n)anda(x,t,u,p)arelocallyH5ldercontinuousonfix(0,co)suchthatwherealtuandparepositiveconstants,m,aZIa3.hi,b2,alIadZ20,or321areconstants,m*E[0,m 2),hi16z/0,afl m*/… 相似文献
6.
Zhigui Lin 《偏微分方程(英文版)》1998,11(3):231-244
This paper deals with the global existence and blow-up of positive solutions to the systems: u_t = ∇(u^∇u) + u¹ + v^a v_t = ∇(v^n∇v) + u^b + v^k in B_R × (0, T) \frac{∂u}{∂η} = u^αv^p, \frac{∂v}{∂η} = u^qv^β on S_R × (0, T) u(x, 0) = u_0(x), v(x, 0} = v_0(x) in B_R We prove that there exists a global classical positive solution if and only if l ≤ l, k ≤ 1, m + α ≤ 1, n + β ≤ 1, pq ≤ (1 - m - α)(1 - n - β),ab ≤ 1, qa ≤ (1 - n - β) and pb ≤ (1 - m - α). 相似文献
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We consider the global existence of classical solutions and blowup phenomena for a spatially one‐dimensional radiation hydrodynamics model problem, which consists of a scalar Burgers‐type equation coupled with a nonlocal advection‐reaction equation for radiation intensity. The model can be seen as an extension of the well‐known Hamer model that includes additionally the effects of scattering. It is well‐known that the initial value problem for Burgers' equation cannot be solved classically as soon as the derivative of the initial datum is negative somewhere. For our model problem, there is a critical negative number such that if the spatial derivative of the initial function is larger than this number, the associated initial‐value problem admits a global classical solution. However, when the spatial derivative of the initial data is below another negative threshold number, the initial value problem can also not be solved classically. Moreover, when there does not exist a global classical solution, it is shown that the first spatial derivative of solution must blow up in finite time. The results of the paper generalize the findings of Kawashima and Nishibata for the Hamer model. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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In this paper, we present a cross-constrained variational method to study the Cauchy problem of the nonlinear Klein-Gordon equations with critical nonlinearity in two space dimensions. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we establish a sharp threshold of global existence and blowup of it. Furthermore, we answer the question： How small are the initial data if the solution exists globally. 相似文献
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In this paper we consider the Elastic membrane equation with memory term and nonlinear boundary damping.Under some appropriate assumptions on the relaxation function h and with certain initial data,the global existence of solutions and a general decay for the energy are established using the multiplier technique.Also,we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping. 相似文献
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§1 IntroductionIn[1],wehaveintroducedtheconceptoftheGclassoffunctionsintheparabolicclass,andhaveprovedtheHldercontinuityofthiskindoffunctions.Theintroductionoftheconceptcontributestotheproofoftheregularityandexistenceofthesolutionforthefirstboundaryvalueproblemofparabolicequationindivergenceform.Here,weconsidertheapplicationsoftheGclassoffunctionsintheparabolicclasstothefirstboundaryvalueproblemofparabolicequation.Asweknow,ithasreceivedextensivestudyforthefirstboundaryvalueproblemofthefoll… 相似文献
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本文考虑带线性坍塌项和竞争势的非线性波动方程柯西问题,定义了新的稳定集和不稳定集,证明了如果初值进入不稳定集,则解在有限时间爆破;如果初值进入稳定集,则整体解存在.运用势井讨论,回答了当初值在多么小的时候,该柯西问题的整体解存在. 相似文献
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In this paper, we study a system of nonlinear coupled wave equations with damping, source, and nonlinear strain terms. We obtain several results concerning local existence, global existence, and finite time blow‐up property with positive initial energy by using Galerkin method and energy method, respectively. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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We study the small‐data Cauchy problem for n‐dimensional Stokes damped Rosenau equation. Under some assumptions, we prove the global existence and uniqueness of the small‐amplitude solution by utilizing the contraction mapping principle and study the asymptotic behavior of the solution. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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We consider a generalization of Camassa–Holm‐type equation including the Camassa–Holm equation and the Novikov equation. We mainly establish the existence of solutions in lower order Sobolev space with . Then, we present a precise blowup scenario and give a global existence result of strong solutions. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Anass Lamaizi Abdellah Zerouali Omar Chakrone Belhadj Karim 《Journal of Nonlinear Modeling and Analysis》2025,7(3):782-793
Our focus in this study revolves around investigating the following parabolic problem $$begin{cases}u_{t}-Delta u +u=0 quad ~ text{ in } ~ Omega ,~ t>0 , frac{partial u}{partial nu }= g(u) quad quad quad quad ~~ text{ on } partial Omega ,~ t>0 , u(x, 0)=u_{0}(x) quad ~~~ text{ in } ~ Omega . end{cases} $$By using the Galerkin approximation and a family of potential wells, we obtain the existence of global solution and finite time blow-up under some suitable conditions. On the other hand, the results for asymptotic behavior of certain solutions with positive initial energy are also given. 相似文献
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Dwijendra N. Pandey Amit Ujlayan 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):3690-3698
In this paper we study a class of fractional order integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness and regularity of a mild solution to these fractional order integrodifferential equations. 相似文献
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Wen‐Shu Zhou 《Mathematical Methods in the Applied Sciences》2008,31(14):1704-1721
This paper is devoted to the existence and regularity of the homogenous Dirichlet boundary value problem for a singular nonlinear elliptic equation with natural growth in the gradient. By certain transformations, the problem can be transformed formally into either a Dirichlet problem or boundary blowup problems without gradient term, for which the corresponding existence results are also derived, which is a partial extension and supplement to the previous works. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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Youpeng Chen 《Applicable analysis》2013,92(7):1495-1510
In this article, we investigate the positive solution of a localized quasilinear parabolic system with nonlocal boundary conditions. Under certain conditions, the global existence and finite time blow-up criteria are established, and the global blow-up behaviour is also obtained. 相似文献