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,⋯.
|Number of pages||28|
|Journal||Advanced Nonlinear Studies|
|Publication status||Published - 2012|