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- W2913579848 abstract "In this paper, we study the blow-up and global existence of solutions to the following time fractional nonlinear diffusion equations $$left{ {begin{array}{*{20}{c}} {mathop 0limits^C D_t^alpha u - Delta u{ = _0}I_t^{1 - gamma }left( {{{left| u right|}^{p - 1}}u} right),;x in {^N},;t > 0,} {uleft( {0,x} right) = {u_0}left( x right),;x in {^N},} end{array}} right.$$ where 0 < α < γ < 1, p > 1, u0 ∈ C0(ℝN), $$_0I_t^theta $$ denotes left Riemann-Liouville fractional integrals of order θ. $$mathop 0limits^C D_t^alpha u = frac{partial }{{partial t}}{}_0I_t^{1 - alpha }left( {uleft( {t,x} right) - uleft( {0,x} right)} right)$$ . Let β = 1 − γ. We prove that if $$1<p<p* = max left{ {1 + frac{beta }{alpha },1 + frac{{2left( {alpha + beta } right)}}{{alpha N}}} right}$$ , the solutions of (1.1) blows up in a finite time. If $$N<frac{{2left( {alpha + beta } right)}}{beta },p ge p*;or;N ge ;frac{{2left( {alpha + beta } right)}}{beta },p > p*$$ , and ∥u0∥Lqc(ℝN) is sufficiently small, where $${q_c} = frac{{Nalpha left( {p - 1} right)}}{{2left( {alpha + beta } right)}}$$ , the solutions of (1.1) exists globally." @default.
- W2913579848 created "2019-02-21" @default.
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- W2913579848 date "2018-12-01" @default.
- W2913579848 modified "2023-09-30" @default.
- W2913579848 title "Blow-up and global existence of solutions for a time fractional diffusion equation" @default.
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- W2913579848 doi "https://doi.org/10.1515/fca-2018-0085" @default.
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