{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:D4XCOV4MGBPHKHQWU66QXGGEYT","short_pith_number":"pith:D4XCOV4M","schema_version":"1.0","canonical_sha256":"1f2e27578c305e751e16a7bd0b98c4c4cd38848880361454c66d053541f5ccb0","source":{"kind":"arxiv","id":"1706.01251","version":1},"attestation_state":"computed","paper":{"title":"Liouville theorems and Fujita exponent for nonlinear space fractional diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Ma","submitted_at":"2017-06-05T09:45:06Z","abstract_excerpt":"We consider non-negative solutions to the semilinear space-fractional diffusion problem $(\\partial_t+(-\\Delta)^{\\alpha/2})u=\\rho(x)u^p$ on whole space $R^n$ with nonnegative initial data and with $(-\\Delta)^{\\alpha/2}$ being the $\\alpha$-Laplacian operator, $\\alpha\\in (0,2)$. Here $p>0$ and $\\rho(x)$ is a non-negative locally integrable function. For $\\rho(x)=1$ we show that the fujita exponent is $p_F=1+\\frac{\\alpha}{n}$ and the Liouville type result for the stationary equation is true for $00$ and $\\rho(x)$ is a non-negative locally integrable function. For $\\rho(x)=1$ we show that the fujita exponent is $p_F=1+\\frac{\\alpha}{n}$ and the Liouville type result for the stationary equation is true for $0