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

V.A. Galaktionov, E. Mitidieri, S.I. Pohozaev

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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 <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 languageEnglish
Pages (from-to)569-596
Number of pages28
JournalAdvanced Nonlinear Studies
Volume12
Issue number3
Publication statusPublished - 2012

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Semilinear Heat Equation
Sign-changing Solutions
Blow-up
Higher Order
thermodynamics
Countable
Range of data
Biharmonic
Blow-up Solution
Similarity Solution
nonlinearity
Bifurcation Point
Fourier coefficients
Fourth Order
Branching
Numerical Study
coefficients
Bifurcation
Nonlinearity

Cite this

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

In: Advanced Nonlinear Studies, Vol. 12, No. 3, 2012, p. 569-596.

Research output: Contribution to journalArticle

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