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 |
|---|---|
| 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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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 journal › Article
}
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 -