Premium
About the concept of measure‐valued solutions to distributed parameter systems
Author(s) -
Roubíček Tomáš,
Hoffmann KarlHeinz
Publication year - 1995
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.1670180902
Subject(s) - mathematics , measure (data warehouse) , partial differential equation , conservation law , variational inequality , heat equation , calculus (dental) , mathematical economics , mathematical analysis , computer science , medicine , dentistry , database
The measure‐valued (mv) solutions are commonly defined in the literature simply by putting Young measures into the respective partial differential equations. Here a few examples of mv‐solutions to evolution problems (conservation laws, fluid dynamics and a so‐called backward‐forward heat problem) are re‐investigated to show that such definitions are not satisfactorily selective, i.e. they admit (sometimes surprisingly) many mv‐solutions apparently without any physical sense. Then an attempt for a selective definition in the case of the backward‐forward heat problem is made, resulting to a certain evolution variational inequality.