{"paper":{"title":"Concentration Phenomenon of Semiclassical States to Reaction-Diffusion Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tianxiang Gou, Zhitao Zhang","submitted_at":"2019-09-12T04:54:46Z","abstract_excerpt":"In this paper, we consider concentration phenomenon of semiclassical states to the following $2M$-component reaction-diffusion system in $\\R \\times \\R^N$, \\begin{align*} \\left\\{ \\begin{aligned} \\partial_t u &=\\eps^2 \\Delta_x u-u-V(x)v + \\partial_v H(u, v),\\\\ \\partial_t v &=-\\eps^2 \\Delta_x v+v + V(x)u - \\partial_u H(u, v), \\end{aligned} \\right. \\end{align*} where $M \\geq 1$, $N \\geq 1$, $\\eps>0$ is a small parameter, $V \\in C^1(\\R^N, \\, \\R)$, $H \\in C^1(\\R^M \\times \\R^M, \\, \\R)$ and $(u, v): \\R \\times \\R^N \\to \\R^M \\times \\R^M$. It is proved that there exist semiclassical states concentrating "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.05453","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.05453/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}