Abstract
We, first, consider the parabolic equation ut = -(-Δ)α/2um + a(x).∇uq + f(t, x)u'p + w(t, x), t > 0, x ∈ ℝN, where (-Δ)α/2 is the α/2-fractional power of the Laplacian - Δ which for 0 < α ≤ 2 stands for impurities and f(t, x) and w(t, x) are given nonnegative functions, and find its critical exponent. Then, we consider the criticality for five systems of strongly coupled parabolic equations, two of them with nonlinear convective terms. Our results answer positively some open problems raised recently by Bandle, Deng, Levine, and Zhang.
Original language | British English |
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Pages (from-to) | 217-243 |
Number of pages | 27 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 268 |
Issue number | 1 |
DOIs | |
State | Published - 1 Apr 2002 |
Keywords
- Blow-up
- Degenerate systems
- Fractal diffusion operator
- Nonlinear reaction-diffusion systems
- Porous media
- Strongly coupled systems