{"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 $0<p\\leq 1+\\frac{\\alpha}{n-\\alpha}$. When $p=1/2$ and $\\rho(x)$ satisfies an integrable condition, there"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01251","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}