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Zur Abhängigkeit der Lösung von u t + ( h ( u )) x = 0 von ihren Anfangswerten
Author(s) -
Wick J.,
Leis R.
Publication year - 1980
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.1670020412
Subject(s) - mathematics , norm (philosophy) , initial value problem , weak solution , regular polygon , space (punctuation) , mathematical analysis , combinatorics , pure mathematics , geometry , political science , law , linguistics , philosophy
The above equation has some remarkable properties. In general a global solution exists in a weak sense only, and this solution is not reversible in time. Furthermore it is known, that the solutions for different initial values can coincide for all t ⩾ t 0 > 0, and the set of the initial values with this property is convex. Conditions assuring that this set contains only one element are given. This means a weak form of time‐reversibility. As a global solution exists only in the weak sense, the classical question concerning dependence of the solution on the initial values needs some modification. This problem is dealt with in suitable L 1 ‐norms. It is shown, that the L 1 ‐norm of the difference of two weak solutions with respect to the space variable does not increase in time.