Abstract
Blow-up problems for quasilinear reaction diffusion equations with weighted nonlocal source
Highlights
We investigate the following quasilinear reaction diffusion equations
The blow-up problems to reaction diffusion equations has been extensively investigated by many researchers
Since Payne and Schaefer [20] introduced a first-order inequality technique and obtained a lower bound for blow-up time, many authors are devoted to the lower bounds of blow-up time for various reaction diffusion problems
Summary
∑ aij(x)uxi νj = g(u) u(x, 0) = u0(x) in Ω × (0, t∗), on ∂Ω × (0, t∗), in Ω, where Ω ⊂ Rn(n ≥ 2) is a bounded star-shaped domain with smooth boundary ∂Ω, nonlocal source satisfies m f (u(x, t)) ≥ a2(u(x, t))p (u(x, t))αdx , and a2, p, α, and m are positive constants. They derived conditions which imply the solution blows up in finite time or exists globally.
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