Geodesic
Generalized functions on the closure of an open set. Application to uniqueness of some characteristic Cauchy problem
Novi Sad Journal of Mathematics, Tome 46 (2016) no. 2.

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To obtain existence and uniqueness when solving some nonlinear characteristic Cauchy problems, we define a special algebra $\mathcal{G}_{\mathcal{O}_{M}% }\left( \overline{\Omega}\right) $ of generalized functions on the closure $\overline{\Omega}$ of an open set $\Omega$ in $\mathbb{R}^{n}$\ constructed from the topological algebra $\mathcal{O}_{M}\left( \overline{\Omega}\right) $ of slowly increasing functions in $\overline{\Omega}$. Moreover other concepts are needed as slow scale elements and point values characterization of elements in $\mathcal{G}_{\mathcal{O}_{M}}\left( \overline{\Omega}\right) $.
Publié le :
DOI : 10.30755/NSJOM.04634
Classification : 35A01, 35A02, 35D99, 35A25, 46F30, 46T30
Keywords: tempered algebras of generalized functions, closure of open set, regularizing process, point values characterizations, nonlinear characteristic problems 
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     title = {Generalized functions on the closure of an open set. {Application} to uniqueness of some characteristic {Cauchy} problem},
     journal = {Novi Sad Journal of Mathematics},
     pages = {163 - 180},
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Victor Dévoué; Jean-André Marti; Hans Vernaeve; Jasson Vindas. Generalized functions on the closure of an open set. Application to uniqueness of some characteristic Cauchy problem. Novi Sad Journal of Mathematics, Tome 46 (2016) no. 2. doi : 10.30755/NSJOM.04634. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.04634/

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