Generalized Function Solutions to Nonlinear Wave Equations with Distribution Initial Data Page: 3
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Kim, Jongchul, Generalized Function Solutions to Nonlinear Wave Equati-
ons with Distribution Initial Data. Doctor of Philosophy (Mathematics), August,
1996, 53 pp., 16 figures, references.
In this study, we consider the generalized function solutions to nonlinear
wave equation with distribution initial data. J. F. Colombeau shows that the initial
value problem
un -Am = F(u)
m(X,0) = Uq
ut(x, 0) = Ml
where the initial data Mo and Mi are generalized functions, has a unique generalized
function solution u. Here we take a specific F and specific distributions Mo, u\ then
inspect the generalized function representatives for the initial value problem solution
to see if the generalized function solution is a distribution or is more singular. Using
the numerical technics, we show for specfic F and specific distribution initial data
Mo, Mi, there is no distribution solution.
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Kim, Jongchul. Generalized Function Solutions to Nonlinear Wave Equations with Distribution Initial Data, dissertation, August 1996; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc278853/m1/3/: accessed July 11, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .