Existence of a classical solution to complex material flow problems

Abstract

An existence result of smooth solutions for a complex material flow problem is provided. The considered equations are of hyperbolic type including a nonlocal interaction term. The existence proof is based on a problem-adapted linear iteration scheme exploiting the structure conditions of the nonlocal term. 35Q70, 35L65Copyright

On the global classical solution to compressible Euler system with singular velocity alignment

“…See [4,28,30] for threshold conditions for the pressureless systems, and [8] for isothermal pressure p(ρ) = ρ with small initial data. For the case where the communication weight is not positive, such as in the pedestrian and material flow case, an additional damping effect is required to prove the global smooth solution for small initial data in [6,32,33].…”

The global classical solution to compressible Euler system with velocity alignment

“…The pressureless Euler system with non-local forces has been studied recently and very limited results have been done. The local existence of classical solutions of the complex material flow dynamics which has been derived in [12], under structural condition for the interaction force has been obtained in [7]. In [4], for the 1-D model with damping and non-local interaction, a critical Date: December 4, 2019.…”

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