This paper is dedicated to Joachim Wick Communicated by H. Neunzert A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new class of solutions is obtained. Tw
A Kinetic Model for Vehicular Traffic: Existence of Stationary Solutions
β Scribed by R. Illner; A. Klar; H. Lange; A. Unterreiter; R. Wegener
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 143 KB
- Volume
- 237
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
of moving swarms. A notion of weak solutions for this hyperbolic chemotaxis model is presented and the global existence of weak solutions is shown. The proof relies on the vanishing viscosity method; i.e., we obtain the weak solution as the limit of classical solutions of an associated parabolically
The system u 1t &2u 1 =u 1 u 2 &bu 1 , u 2t &2u 2 =au 1 in 0\_(0, T), where 0/R n is a smooth bounded domain, with homogeneous Dirichlet boundary conditions u 1 = u 2 =0 on 0\_(0, T) and initial conditions u 1 (x, 0), u 2 (x, 0), is studied. First, it is proved that there is at least one positive st
## Abstract In this article we discuss the local existence and uniqueness of solutions of a system of parabolic differential partial equations modeling the process of solidification/melting of a certain kind of alloy. This model governs the evolution of the temperature field, as well as the evoluti