JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (1): 123-127.doi: 10.6040/j.issn.1671-9352.0.2015.003

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Nehari manifold and application to blow-up for a class of semilinear parabolic equations

LIU Yang, DA Chao-jiu, LI Fu-ming   

  1. College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, Gansu, China
  • Received:2015-01-12 Online:2016-01-16 Published:2016-11-29

Abstract: The initial boundary value problem for a class of semilinear parabolic equations with positive initial energy is studied. The finite time blow-up of solutions is obtained by the Nehari manifold and the convexity method. Moreover, the relationship between initial energy and finite time blow-up of solutions is described.

Key words: semilinear parabolic equations, finite time blow-up, Nehari manifold

CLC Number: 

  • O175.24
[1] BUDD C, DOLD B, STUART A. Blow-up in a system of partial differential equations with conserved first integral II Problems with convection[J]. SIAM J Appl Math, 1994, 54(3):610-640.
[2] EI SOUFI A, JAZAR M, MONNEAU R. A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions[J]. Ann I H Poincaré-AN, 2007, 24(1):17-39.
[3] JAZAR M, KIWAN R. Blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions[J]. Ann I H Poincaré-AN, 2008, 25(2):215-218.
[4] GAO Wenjie, HAN Yuzhu. Blow-up of a nonlocal semilinear parabolic equation with positive initial energy[J]. Appl Math Lett, 2011, 24(5):784-788.
[5] ALVES C O, EL HAMIDI A. Nehari manifold and existence of positive solutions to a class of quasilinear problems[J]. Nonlinear Anal-Theor, 2005, 60(4):611-624.
[6] AMBROSETTI A, RABINOWITZ P H. Dual variational methods in critical point theory and applications[J]. J Funct Anal, 1973, 14(4):349-381.
[7] MO Haiping, LIU Yang, YU Tao. Continuity of depth functions of potential well family for a class of nonlinear wave equations[J]. Mathematica Applicata, 2011, 24(1):126-130.
[1] SUN Guo-wei, MAI A-li. Multiple homoclinic solutions for second order nonlinear difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 51-54.
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