{"paper":{"title":"Decay of large solutions around shocks to multi-D viscous conservation law with strictly convex flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"HyeonSeop Oh, Moon-Jin Kang","submitted_at":"2025-01-08T07:01:15Z","abstract_excerpt":"We consider a planar viscous shock for a scalar viscous conservation law with a strictly convex flux in multi-dimensional setting, where the transversal direction is periodic. We first show the contraction property for any solutions evolving from a large bounded initial perturbation in $L^2$ of the viscous shock. The contraction holds up to a dynamical shift, and it is measured by a weighted relative entropy. This result for the contraction extends the existing result in 1D \\cite{Kang19} to the multi-dimensional case. As a consequence, if the large bounded initial $L^2$-perturbation is also in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04311","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.04311/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"}