Exam (elaborations)
New Results on the Burgers and the Linear Heat Equations in Unbounded Domain
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Given u0 ∈ L 1 loc(0, +∞), u0(x) ≥ 0 a.e. x ∈ (0, +∞), we consider the viscous Burgers’ problem (V BP) ut − uxx + uux = 0 x ∈ (0, +∞), t > 0, u(0,t) = 0 lim infx→∞ u(t, x) ≥ 0t > 0, u(x, 0) = u0(x) on (0, +∞). (1) Our goal is to prove tha...
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