Question: Partial differential equations 1.* Use the Fourier transform to solve the initial value problem 14 - Uxx + Ux = 0, X ER, t> 0,

Partial differential equations

1.* Use the Fourier transform to solve the initial value problem 14 - Uxx + Ux = 0, X ER, t> 0, u(x, 0) = g(x), xER, where g E L'(R). 2. Consider the fundamental solution of the heat equation in R", H(x, t) := ( Arkin/ze al , t > 0, 0, 1 co.)

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