### Abstract

2, with non-monotone nonlinearity u = -(-δ) u + |u| in ℝ × R , in the range 1 <p ≤ p = 1 + 2m/n, (0.2) with the same initial data u . The fourth order biharmonic case m = 2 is studied in greater detail. The blow-up Fujita-type result for (0.2) now reads as follows: blow-up occurs for any initial data u with positive first Fourier coefficient: (Equation presented) i.e., as for (0.1), any such arbitrarily small initial function u (x) leads to blow-up. The construction of two countable families of global sign changing solutions is performed on the basis of bifurcation/branching analysis and a further analytic-numerical study. In particular, a countable sequence of bifurcation points of similarity solutions is obtained: p =1 + 2m/N+l′ l= 0,1,2,⋯.

Original language | English |
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Pages (from-to) | 569-596 |

Number of pages | 28 |

Journal | Advanced Nonlinear Studies |

Volume | 12 |

Issue number | 3 |

Publication status | Published - 2012 |

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### Cite this

*Advanced Nonlinear Studies*,

*12*(3), 569-596.

**Global sign-changing solutions of a higher order semilinear heat equation in the subcritical fujita range.** / Galaktionov, V.A.; Mitidieri, E.; Pohozaev, S.I.

Research output: Contribution to journal › Article

*Advanced Nonlinear Studies*, vol. 12, no. 3, pp. 569-596.

}

TY - JOUR

T1 - Global sign-changing solutions of a higher order semilinear heat equation in the subcritical fujita range

AU - Galaktionov, V.A.

AU - Mitidieri, E.

AU - Pohozaev, S.I.

PY - 2012

Y1 - 2012

N2 - A detailed study of two classes of oscillatory global (and blow-up) solutions was began in [20] for the semilinear heat equation in the subcritical Fujita range u = δu + |u| u in ℝ × ℝ for 1 2, with non-monotone nonlinearity u = -(-δ) u + |u| in ℝ × R , in the range 1

AB - A detailed study of two classes of oscillatory global (and blow-up) solutions was began in [20] for the semilinear heat equation in the subcritical Fujita range u = δu + |u| u in ℝ × ℝ for 1 2, with non-monotone nonlinearity u = -(-δ) u + |u| in ℝ × R , in the range 1

UR - http://www.scopus.com/inward/record.url?scp=84867809563&partnerID=8YFLogxK

UR - http://www.advancednonlinearstudies.com/

M3 - Article

VL - 12

SP - 569

EP - 596

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

SN - 1536-1365

IS - 3

ER -