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Lax-Ole˘ınik explicit formula and structure theory for balance laws
فرمول صریح و نظریه Lax-Ole˘ınik برای تعادل قوانین -2020 source term having the form
ut +f (u)x − α(t)u =0 inR×(0,∞)
u(x, 0) = u0 on R × {t = 0}.
Consequently, we show that the behaviour of the shock packets and the phenomenon of one shock situation is completely different when compared to equations without a source term. Moreover, contrary to the be-haviour of shock packets in conservation laws, in our situation, we show that the slope of the left boundary of the shock packet can be strictly greater than that of the right boundary. Keywords:Balance laws | Riemann problem | Hamilton-Jacobi equation | Structure theorem | Asymptotically single shock packet | Lax-Ole˘ınik Formula |
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