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On the Long‐time Behaviour of Solutions to a Conservation Law with Memory
Author(s) -
Feireisl Eduard,
Petzeltová Hana
Publication year - 1997
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/(sici)1099-1476(19970510)20:7<569::aid-mma862>3.0.co;2-m
Subject(s) - conservation law , convexity , mathematics , geodetic datum , scalar (mathematics) , infinity , mathematical economics , law , mathematical analysis , calculus (dental) , pure mathematics , mathematical physics , geometry , political science , geology , economics , medicine , dentistry , financial economics , geodesy
We show that any solution of the scalar conservation law(u+k*u) t +σ(u) x =0starting from spatially periodic initial datum stabilizes to its integral mean as time goes to infinity. No convexity or ‘genuinely non‐linear’ like conditions are assumed concerning σ. © 1997 by B. C. Teubner stuttgart–John Wiley & Sons Ltd.