منابع مشابه
Systems of Hyperbolic Conservation Laws with Memory
Global weak solutions of bounded variation to systems of balance laws with non-local source are constructed by the method of vanishing viscosity. Suitable dissipativeness assumptions are imposed on the source terms to assure convergence of the method. Under these hypotheses, the total variation remains uniformly bounded and integrable in time, the vanishing viscosity solutions are uniformly sta...
متن کاملHyperbolic Conservation Laws with Fading Memory
Ut + F (U)x = 0 correspond to the constitutive relations of an elastic medium if the flux F is determined by the value of the conserved quantity U(x, t). However, if viscosity or relaxation phenomena are present, this model is inadequate. In such a case, the flux depends also on the past history of the medium U(x, τ) for τ < t, i.e., the material has memory. An important class of media of this ...
متن کاملSystems of conservation laws with dissipation
2 Systems of conservation laws have the form ∂ t u+div x q = 0. They describe processes in many situations of the real life, including continuum mechanics. A system is in closed form when the flux q is given in terms of u. An algebraic equation of state q := f (u) yields a quasilinear first-order system. But a more accurate description involves a dissipative mechanism, through various additiona...
متن کاملConservation laws and Hamilton’s equations for systems with long-range interaction and memory
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action principle: generalized Noether’s theorem and Hamiltonian type equations. In the first case, we derive conservation laws in the form of continuity equations that c...
متن کاملInvariant Regions for Systems of Conservation Laws
We describe necessary and sufficient conditions for a region in R." to be invariant for (Glimm) solutions of the system of n conservation laws Ut + f(u)x = 0. We also make some observations about the invariance of such regions for certain finite difference approximations of solutions of systems of conservation laws.
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 1988
ISSN: 0895-7177
DOI: 10.1016/0895-7177(88)90662-0