caa a22 4500 477076971 CHVBK 20180405111440.0 cr unu---uuuuu 170330e19961101xx s 000 0 eng 10.1007/BF00047123 doi (NATIONALLICENCE)springer-10.1007/BF00047123 Generalized solutions to partial differential equations of evolution type [Elektronische Daten] [J. Colombeau, A. Heibig, M. Oberguggenberger] This paper deals with a new solution concept for partial differential equations in algebras of generalized functions. Introducing regularized derivatives for generalized functions, we show that the Cauchy problem is wellposed backward and forward in time for every system of linear partial differential equations of evolution type in this sense. We obtain existence and uniqueness of generalized solutions in situations where there is no distributional solution or where even smooth solutions are nonunique. In the case of symmetric hyperbolic systems, the generalized solution has the classical weak solution as ‘macroscopic aspect'. Two extensions to nonlinear systems are given: global solutions to quasilinear evolution equations with bounded nonlinearities and local solutions to quasilinear symmetric hyperbolic systems. Kluwer Academic Publishers, 1996 algebras of generalized functions nationallicence generalized derivatives nationallicence linear and nonlinear partial differential equations of evolution type nationallicence existence and uniqueness of solutions nationallicence symmetric hyperbolic systems nationallicence Colombeau J. Ecole Normale Supérieure de Lyon, F69364, Lyon, France aut Heibig A. Ecole Normale Supérieure de Lyon, F69364, Lyon, France aut Oberguggenberger M. Universität Innsbruck, A6020, Innsbruck, Austria aut Acta Applicandae Mathematica Kluwer Academic Publishers 45/2(1996-11-01), 115-142 0167-8019 45:2<115 1996 45 10440 https://doi.org/10.1007/BF00047123 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00047123 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Colombeau J. Ecole Normale Supérieure de Lyon, F69364, Lyon, France aut NATIONALLICENCE 700 1- Heibig A. Ecole Normale Supérieure de Lyon, F69364, Lyon, France aut NATIONALLICENCE 700 1- Oberguggenberger M. Universität Innsbruck, A6020, Innsbruck, Austria aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 45/2(1996-11-01), 115-142 0167-8019 45:2<115 1996 45 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer