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- W2951499038 abstract "We show non-existence of solutions of the Cauchy problem in $mathbb{R}^N$ for the nonlinear parabolic equation involving fractional diffusion $partial_t u + (-Delta)^s phi(u)= 0,$ with $0 0$, or $phi(u) = log u$, and we take nonnegative $L^1$ initial data, there is no (nonnegative) solution of the problem in any dimension $Nge 2$. We find the range of non-existence when $N=1$ in terms of $s$ and $n$. The range of exponents that we find for non-existence both for parabolic and elliptic equations are optimal. Non-existence is then proved for more general nonlinearities $phi$, and it is also extended to the related elliptic problem of nonlinear nonlocal type: $u + (-Delta)^s phi(u) = f$ with the same type of nonlinearity $phi$." @default.
- W2951499038 created "2019-06-27" @default.
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- W2951499038 date "2015-05-12" @default.
- W2951499038 modified "2023-09-27" @default.
- W2951499038 title "Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations" @default.
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