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math.AP2026
Local Asymptotic Patterns for Viscous Approximations of Conservation Laws
Alberto Bressan, Laura Caravenna, Wen Shen
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximatio…
math.AP2026
Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
Le Chen, Ian Ruau, Wenxian Shen
This paper is Part II of a series on boundedness, global existence, and asymptotic behavior of positive classical solutions to the chemotaxis model $$\begin{cases} u_t=Δu-χ_0\nabla…
math.AP2026
A Uniqueness Condition for Conservation Laws with Discontinuous Gradient-Dependent Flux
Alberto Bressan, Wen Shen
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions or , when th…