a) Find a weak formulation for the partial differential equation∂u∂t +c∂u∂x =0b) Show that u=f(x−ct) is a generalized solution of∂u∂t +c∂u∂x =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(∂u∂t +c∂u∂x )∗ϕ(x)dx==∫Ω∂u∂tϕ(x)dx−c∫Ωu(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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a) Find a weak formulation for the partial differential equation∂u∂t +c∂u∂x =0b) Show that u=f(x−ct) is a generalized solution of∂u∂t +c∂u∂x =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&#039;s take any test function ϕ, then we have (integrating by parts second part of the integral)∫Ω(∂u∂t +c∂u∂x )∗ϕ(x)dx==∫Ω∂u∂tϕ(x)dx−c∫Ωu(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?

Tate Puckett · Accepted Answer

a.) The idea of integral solutions is a little more complicated than just integration with a test function. Its

koffiejkl · Accepted Answer

b.) Use the weak formulation to integrate u=f(x−ct). Youre

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

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