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关于一类分数阶扩散型方程解的适定性 被引量：1

Well-posedness to a class of dissipative-type equation with anomalous diffusion
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摘要 应用Young不等式、插值不等式和压缩映像原理,研究了一类分数阶耗散型方程解的存在唯一性,得到当初值足够小时,相应的非线性初值问题存在唯一解属于L∞(RN)或L1(RN)∩L∞(RN). In this paper,by applying Young inequality,interpolation inequality and contraction mapping principle,we studied a class of fractional dissipation type equations.When the initial value is small enough,the initial value problem to the nonlinear equation has a unique solution in the spaces L∞（RN）or L1（RN）∩L∞（RN）.
作者 王法有 魏素青 刘玉娟
机构地区 河南理工大学数学与信息科学学院
出处 《河南理工大学学报（自然科学版）》 CAS 2011年第6期745-748,共4页 Journal of Henan Polytechnic University（Natural Science）
基金 河南省高校科技创新人才支持计划项目(2009HASTIT007) 河南省杰出青年计划项目(101400510015) 河南理工大学青年基金资助项目(Q2010-38)
关键词 分数阶扩散型方程 适定性 压缩映像原理 Dissipative-type equation well-posedness Contraction mapping principle
分类号 O175.2 [理学—基础数学]
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参考文献10

  • 1KARCH G,WOYCZYNSKI W A.Fractal Hamilton-Jacobi-KPZ equations[J].Trans Amer Math Soc,2008,360:2423-2442.
  • 2BILER P,KARCH G,WOYCZYNSKI W A.Asymptotics for conservation laws involving Levy diffusion generator[J].Studia Math,2001,148:171-192.
  • 3KARCH G,MIAO C,XU X.On convergence of solutions of fractal burgers equation toward rarefaction waves[J].SiamJ Math Anal,2008,39:1536-1549.
  • 4BILER P,FUNAKI T,WLYCZYNSKI W A.Fractal Burgers equations[J].J Differential Equations,1998,148:9-46.
  • 5GILDING B H.The cauchy problem for large-time behaviour[J].J Math Pures Appl,2005,84:753-785.
  • 6DRONIOU J,IMBERT C.Fractal first order partial differential equations[J].Arch Rational Mech Anal,2006,182:299-331.
  • 7边东芬,胡越.耗散型聚合方程组Cauchy问题的适定性[J].河南理工大学学报（自然科学版）,2011,30(2):233-238. 被引量：3
  • 8PINSKY R G,Existence and nonexistence of global solutions[J].J Differential Equations,1997,133:152-177.
  • 9AMOUR L,BEN ARTZI M.Global existence and decay for viscous Hamilton-Jacobi equations[J].Nonliear Anal,1998,31:621-628.
  • 10BILER P,KARCH G,WOYCZYNSKI W A.Critical nonlinearity exponent and self-similar asymptotics for Lévy conser-vation laws[J].Poincare-Analyse nonlineare,2001,18:613-637.

二级参考文献12

  • 1PIOTR BILER,GRZEGORZ KARCH,PHILIPPE LAURENCOT.Blowupof solutions to diffusion aggregation model[J]-Nonlinearity,2009,22:1559-1568.
  • 2PIOTR BILER,TADAHISA FUNAKI,WOJBOR A,et al.Fractal Burgers equations[J].Dif-ferential Equations,1998,148:9-46.
  • 3PIOTR BILER,WOJBOR A.Global and exploding solutions for nonlocal quadratic evolution problems[J].SIAM J Appl Math,1998,59:845 -869.
  • 4PIOTR BILER,GANG WU.Two -dimensionalchemotaxis models with fractionaldiffusion[J].Math Methods Appl Sciences,2009,32:112-126.
  • 5CARLOS ESCUDERO.The fractional Keller-Segel model[J].Nonlinearity,2006,19:2909 -2918.
  • 6DONG LI,JOSE L.RODRIGO.Finite-time singularities of an aggregation equation in Rn with fractional dissipation[J],Comm Math Phys,2009,287:687-703.
  • 7ANDREAL BERTOZZI,THOMAS LAURENT.Finite-time blow-up of solutions of an aggregation equation in Rn[J].Commun Math Phys,2007,274:717 -735.
  • 8THOMAS LAURENT.Localandglobal existence for an aggregation equation[J].Commun Partial Differential Equations,2007,32:1941-1964.
  • 9CHANGXING MIAO,BAOQUAN YUAN,BO ZHANG.Well-posedness of the Cauchy problem for the fractional power dissipative equations[J].Nonlinear Analysis,2008,68:461 -484.
  • 10TAKASHI KATO.Strong Lp solutions of the Navier-Stokes equations in Rm with applications[J].Math Z,1984,187:471 -480.

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河南理工大学学报（自然科学版）
2011年 第6期

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