a) Find a weak formulation for the partial differential equation{\partial u\over\partial t

rhita3yp 2022-02-18 Answered
a) Find a weak formulation for the partial differential equationut +cux =0b) Show that u=f(xct) is a generalized solution ofut +cux =0for any distribution fWhat i already haveI know that in order to find a weak form of a pde, we need to multiply it by a test function, then integrate it. Also, to find a generalized solution, we need to find a weak solution and just multiply it by the Heaviside function.Let's take any test function ϕ, then we have (integrating by parts second part of the integral)Ω(ut +cux )ϕ(x)dx==Ωutϕ(x)dxcΩu(x,t)ϕ(x)dxwhere ϕ vanishes at boundaries. So, is it the final form or can we proceed further? And how am I supposed to find a generalized solution?
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Tate Puckett
Answered 2022-02-19 Author has 6 answers
a.) The idea of integral solutions is a little more complicated than just integration with a test function. Its
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koffiejkl
Answered 2022-02-20 Author has 7 answers
b.) Use the weak formulation to integrate u=f(xct). Youre
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