Solve the pure IVP for the Burgers pde (1.2) with initial condition (u(0, x)=u_{0}(x) in L_{mathcal{D}}^{2} cap

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Solve the pure IVP for the Burgers pde (1.2) with initial condition \(u(0, x)=u_{0}(x) \in L_{\mathcal{D}}^{2} \cap C_{\mathcal{D}}^{\infty}, \mathcal{D}=(-\infty, \infty)\), using the Hopf-Cole transformation (1.3).

Pde (1.2)

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Eq  (1.3)

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