Giacomo Maria Leccese

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20202026

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math.AP2026

Existence and Blow-Up for Non-linear Fokker-Planck with Controlled Drift

Giacomo Maria Leccese

We extend the global existence results for critical parameters of [Bianchini and Leccese, J. Math. Anal. Appl. (2024)] to the multidimensional problem \begin{equation*} \partial_t…

math.AP2026

Existence and Blow-Up for Nonlinear Fokker-Planck with Controlled Drift Divergence

Giacomo Maria Leccese

We extend the global existence results for critical parameters of [Bianchini and Leccese, J. Math. Anal. Appl. (2024)] to the multidimensional problem \begin{equation*} \partial_t…

math.AP2023

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

Stefano Bianchini, Giacomo Maria Leccese

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 comple…