Errors in approximate solutions of Cauchy's problem for a first-order quasilinear equation |
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Authors: | V G Sushko |
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Institution: | (1) M. V. Lomonosov Moscow State University, USSR |
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Abstract: | The proximity is investigated of the solution of Cauchy's problem for the equation u
t
+( (u ))x= u
xx
(![phiv](/content/j44w513w88735005/xxlarge981.gif) (u ) > 0) to the solution of Cauchy's problem for the equation ut+ ( (u))x= 0, when the solution of the latter problem has a finite number of lines of discontinuity in the strip 0 t T. It is proved that, everywhere outside a fixed neighborhood of the lines of discontinuity, we have |u –u| C , where the constant C is independent of . Similar inequalities are derived for the first derivatives of u –u.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 309–320, September, 1970.In conclusion we express our gratitude to L. A. Chudov for his valuable advice concerning this work. |
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