We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The critical exponent for a time fractional diffusion equation with nonlinear memory.
- Authors
Zhang, Quanguo; Li, Yaning
- Abstract
In this paper, we determine the Fujita critical exponent of the following time fractional subdiffusion equation with nonlinear memory 0CDtαu−△u=0It1−γ|u|p−1u,x∈RN,t>0,u(0,x)=u0(x),x∈RN,where 0 < α < 1, 0 ≤ γ < 1, γ ≤ α, p > 1, u0∈C0RN, 0It1−γ denotes left Riemann‐Liouville fractional integral of order 1 − γ. Let β = 1 − γ. We prove that, if 1<p≤p∗=max1+2(α+β)2+αN−2(α+β)+,1γ, any nontrivial positive solution blows up in a finite time. If p > p∗ and ‖u0‖LqcRN is sufficiently small, where qc=Nα(p−1)2(α+β), then u exists globally.
- Subjects
NONLINEAR systems; FUJITA Scale; FRACTIONAL differential equations; INTEGRAL equations; CAUCHY problem
- Publication
Mathematical Methods in the Applied Sciences, 2018, Vol 41, Issue 16, p6443
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.5169