{"paper":{"title":"Initial value problems in Clifford-type analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CV","authors_text":"Carmen J. Vanegas, Yanett M. Bol\\'ivar","submitted_at":"2011-06-18T03:42:57Z","abstract_excerpt":"We consider an initial value problem of type $$ \\frac{\\partial u}{\\partial t}={\\cal F}(t,x,u,\\partial_j u), \\quad u(0,x)=\\phi(x), $$ where $t$ is the time, $x \\in \\mathbb{R}^n $ and $u_0$ is a Clifford type algebra-valued function satisfying ${\\bf D}u=\\displaystyle\\sum_{j=0}^{n}\\lambda_j(x)e_j\\partial_ju = 0$, $\\lambda_j(x)\\in \\mathbb{R} $ for all $j$. We will solve this problem using the technique of associated spaces. In order to do that, we give sufficient conditions on the coefficients of the operators ${\\cal F}$ and ${\\bf D}$, where ${\\cal F}(u)= \\displaystyle\\sum_{i=0}^{n}A^{(i)}(x)\\disp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3611","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"}