Generalized Function Solutions to Nonlinear Wave Equations with Distribution Initial Data

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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 u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 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 specific ... continued below

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v, 53 leaves : ill.

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Kim, Jongchul August 1996.

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  • Kim, Jongchul

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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 u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 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 specific F and specific distribution initial data u_0, u_1, there is no distribution solution.

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v, 53 leaves : ill.

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UNT Theses and Dissertations

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  • August 1996

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  • March 26, 2014, 9:30 a.m.

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  • July 20, 2015, 8:25 a.m.

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Kim, Jongchul. Generalized Function Solutions to Nonlinear Wave Equations with Distribution Initial Data, dissertation, August 1996; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc278853/: accessed June 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .