caa a22 4500 445869410 CHVBK 20180317145507.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00605-010-0232-x doi (NATIONALLICENCE)springer-10.1007/s00605-010-0232-x Hörmann Günther Fakultät für Mathematik, Universität Wien, Wien, Austria aut The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data [Elektronische Daten] [Günther Hörmann] We set-up and solve the Cauchy problem for Schrödinger-type differential operators with generalized functions as coefficients, in particular, allowing for distributional coefficients in the principal part. Equations involving such kind of operators appeared in models of deep earth seismology. We prove existence and uniqueness of Colombeau generalized solutions and analyze the relations with classical and distributional solutions. Furthermore, we provide a construction of generalized initial values that may serve as square roots of arbitrary probability measures. Springer-Verlag, 2010 Colombeau generalized functions nationallicence Generalized solutions of differential equations nationallicence Monatshefte für Mathematik Springer Vienna 163/4(2011-08-01), 445-460 0026-9255 163:4<445 2011 163 605 https://doi.org/10.1007/s00605-010-0232-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0232-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hörmann Günther Fakultät für Mathematik, Universität Wien, Wien, Austria aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 163/4(2011-08-01), 445-460 0026-9255 163:4<445 2011 163 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer