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arXiv · 2311.09982

Existence and Blow-up for Non-autonomous Scalar Conservation Laws With Viscosity

Stefano Bianchini·Giacomo Maria Leccese
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Abstract

We consider a question posed in [GSZZ22], namely the blow-up of the PDE $$u_t + (b(t,x) u^{1+k})_x = u_{xx}$$ 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 $b \in L^{p,\infty}$, $p \in (2,\infty]$, or $b_x \in L^{p,\infty}$, $p \in (1,\infty]$.

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Stefano Bianchini, Giacomo Maria Leccese. 2023-11-16. Existence and Blow-up for Non-autonomous Scalar Conservation Laws With Viscosity. https://arxiv.org/abs/2311.09982

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