{"paper":{"title":"Accelerating fronts in semilinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bernardo Galv\\~ao-Sousa, Robert L. Jerrard","submitted_at":"2013-01-23T19:21:05Z","abstract_excerpt":"We study dynamics of interfaces in solutions of the equation $\\epsilon \\Box u + \\frac 1 \\epsilon f_\\epsilon(u)=0$, for $f_\\epsilon$ of the form $f_\\epsilon(u) = (u^2-1)(2u- \\epsilon\\kappa)$, for $\\kappa\\in {\\mathbb R}$, as well as more general, but qualitatively similar, nonlinearities. We consider equations of this form both in $(1+n)$-dimensional Minkowski space, $n\\ge 1$, and on certain more general Lorentzian manifolds, and we prove that for suitable initial data, solutions exhibit interfaces that sweep out timelike hypersurfaces of mean curvature proportional to $\\kappa$. In particular, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5609","kind":"arxiv","version":2},"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"}