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Non Local Conservation Laws in Bounded Domains
Elena Rossi,Rinaldo M. Colombo +1 more
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The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided.Abstract:
The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to define a non local operator adapted to the presence of a boundary. Numerical integrations show that the resulting model provides qualitatively reasonable solutions.read more
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Dissertation
Non-local conservation laws for traffic flow modeling
TL;DR: This thesis proves the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling, and proposes alternative simple schemes to numerically integrate non- local multi- class systems in one space dimension.
Journal ArticleDOI
Sharp critical thresholds for a class of nonlocal traffic flow models
Thomas J. Hamori,Changhui Tan +1 more
TL;DR: In this paper , a class of traffic flow models with non-local look-ahead interactions was studied, and sharp critical threshold conditions were obtained to distinguish the initial data into a trichotomy: subcritical initial conditions lead to global smooth solutions, while two types of supercritical initial condition lead to two kinds of finite time shock formations.
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Asymptotically compatibility of a class of numerical schemes for a nonlocal traffic flow model
Kuang Huang,Qiang Du +1 more
TL;DR: In this paper , numerical discretization of a nonlocal conservation law was considered for vehicular traffic flows involving nonlocal inter-vehicle interactions.
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Analysis of District Heating Networks
TL;DR: In this paper , a model for the distribution of energy through water (for heating or cooling) from a central power station to the consumers is considered, and the authors prove the well posedness of the system by using the Banach Fixed Point Theorem together with stability estimates for reduced systems.
References
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Book ChapterDOI
Elliptic Partial Differential Equations of Second Order
Piero Bassanini,Alan R. Elcrat +1 more
TL;DR: In this paper, a class of partial differential equations that generalize and are represented by Laplace's equation was studied. And the authors used the notation D i u, D ij u for partial derivatives with respect to x i and x i, x j and the summation convention on repeated indices.
Book
Minimal surfaces and functions of bounded variation
TL;DR: In this article, a priori estimation of the gradient of the Bernstein problem is given. But the gradient is not a priorimate of the radius of the singular set, and it is not known whether the gradient can be estimated by direct methods.
Book
Weak and Measure-Valued Solutions to Evolutionary PDEs
TL;DR: In this article, a concise treatment of the theory of nonlinear evolutionary partial differential equations is provided, and a rigorous analysis of non-Newtonian fluids is provided for applications in physics, biology, and mechanical engineering.
Journal ArticleDOI
Self-Organizing Pedestrian Movement
TL;DR: The dynamics of pedestrian crowds is surprisingly predictable and the corresponding computer simulations are a valuable tool for developing optimized pedestrian facilities and way systems.
Journal ArticleDOI
First order quasilinear equations with boundary conditions
TL;DR: In this article, the initial and boundary condition problem for a general first order quasilinear equation in several space variables was solved by using a vanishing viscosity method and gave a definition which chara...
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