EXISTENCE AND BLOW-UP FOR NON-AUTONOMOUS SCALAR CONSERVATION LAWS WITH VISCOSITY
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Date
2023-11-23
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Abstract
We consider a question posed in [1], namely the blow-up of the PDE
ut + (b(t, x)u1+k)x = uxx
when b is uniformly bounded, Lipschitz and k = 2. We give a complete answer to the behavior of
solutions when b belongs to the Lorentz spaces b ∈ Lp,∞, p ∈ (2,∞], or bx ∈ Lp,∞, p ∈ (1,∞].
Description
SISSA 15/2023/MATE