{"paper":{"title":"Nonlinear evolution PDEs in R^+ \\times C^d: existence and uniqueness of solutions, asymptotic and Borel summability","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"O. Costin, S. Tanveer","submitted_at":"2006-08-11T17:50:38Z","abstract_excerpt":"We consider a system of $n$-th order nonlinear quasilinear partial differential equations of the form\n  $${\\bf u}_t + \\mathcal{P}(\\partial_{\\bf x}^{\\bf j}){\\bf u}+{\\bf g} \\left( {\\bf x}, t, \\{\\partial_{\\bf x}^{{\\bf j}} {\\bf u}\\}) =0; {\\bf {u}}({\\bf x}, 0) = {\\bf {u}}_I({\\bf x})$$\n with $\\mathbf{u}\\in\\CC^{r}$, for $ t\\in (0,T)$ and large $|{\\bf x}|$ in a poly-sector $S$ in $\\mathbb{C}^d$ ($\\partial_{\\bf x}^{\\bf j} \\equiv \\partial_{x_1}^{j_1} \\partial_{x_2}^{j_2} ...\\partial_{x_d}^{j_d}$ and $j_1+...+j_d\\le n$). The principal part of the constant coefficient $n$-th order differential operator $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608290","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"}