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具源项和正初始能量的拟线性抛物方程解的不存在性(英文) 被引量：1

Global Nonexistence for a Class of Quasilinear Parabolic Equation with Source Termand Positive Initial Energy
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摘要 利用位势井方法和凸性方法得到了一类具源项和正初始能量的拟线性抛物方程解的不存在性,推广了已知结果. The blow-up of solution for a class of quasilinear parabolic equation with source term and positive initial energy is studied by the well potential and the cocavity methods. The results extend to earlier known works.
作者 庞进生 呼青英
机构地区 商丘职业技术学院 河南工业大学数学系
出处 《河南大学学报（自然科学版）》 CAS 北大核心 2007年第5期448-451,共4页 Journal of Henan University:Natural Science
基金 The National Natural Science Foundation of China(10671182) The Natural Science Foundation of Henan Province(0611053300,200510463024)
关键词 拟线性抛物方程 不存在性 势井 quasilinear parabolic equation blow up potential well
分类号 O175.26 [理学—基础数学]
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参考文献9

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同被引文献14

  • 1Jiang Z,Zheng S,Song S.Blow-up analysis for a nonlinear diffusion equation with nonlinear boundary conditions[J].Appl Math Lett,2004,17(2):193-199.
  • 2Deng K,Levine H A.The role of critical exponents in blow-up theorems:The sequel[J].J Math Anal Appl,2000,243(1):85-126.
  • 3Levine H A.Some nonexistence and instability theorems for solutions of formally parabolic equations of the formPut=-Au+F(u)[J].Archive for Rational Mechanics and Analysis,1973,51(3):371-386.
  • 4Kalantarov V K,Ladyzhenskaya O A.The occurrence of collapse for quasilinear equations of parabolic and hyperbolic type[J].Journal of Soviet Mathematics,1978,10(1):53-70.
  • 5Levine H A,Park S R,Serrin J M.Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type[J].Journal of Differential Equations,1998,142(2):212-229.
  • 6Liu W J,Wang M X.Blow-up of the solution for a p-Laplacian equation with positive initial energy[J].Acta Applicandae Mathematicae,2008,103(1):141-146.
  • 7Messaoudi S A.Blow-up of solutions of a semilinear heat equation with a memory term[J].Abstract and Applied Analysis,2002,2(1):87-94.
  • 8Messaoudi S A.Blow-up of solutions of a semilinear heat equation with a visco-elastic term[J].Progress in Nonlinear Differential Equations and Their Applications,2005,64(1):351-356.
  • 9Messaoudi S A,Tellab B.A general decay result in a quasilinear parabolic system with viscoelastic term[J].Applied Mathematics Letters,2012,25(2):443-447.
  • 10Liu G W,Chen Hua.Global and blow-up of solutions for a quasilinear parabolic system with viscoelastic and source terms[J].Math Meth Appl Sci,2014,37(1):148-156.

引证文献1

河南大学学报（自然科学版）
2007年 第5期

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