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Young measure solutions of some nonlinear mixed‐type equations
Author(s) -
Gittel HansPeter
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1306
Subject(s) - mathematics , discretization , partial differential equation , transonic , measure (data warehouse) , nonlinear system , type (biology) , mathematical analysis , flow (mathematics) , aerodynamics , geometry , ecology , physics , quantum mechanics , database , computer science , engineering , biology , aerospace engineering
This contribution deals with measure‐valued solutions to two types of nonlinear partial differential equations for which, in general, the results on the existence of classical or weak solutions fail. These are the potential equation for transonic flow and the associated unsteady problem (forward–backward diffusion equation). The solutions are constructed by an iteration scheme (Katchanov method) and additional time discretization (Rothe method) in the second case. The existence is proved in the sense of spatial gradient Young measures. Copyright © 2010 John Wiley & Sons, Ltd.