Uniqueness and continuous dependence for systems of balance laws with dissipation

Hyperbolic Balance Laws with a Non Local Source

“…Similarly, the characterization 4 of the tangent vector imply that the present solutions coincide with those in [2].…”

“…To obtain our results we exploit the techniques in [2,9], essentially based on the fractional step algorithm, see [9,10,13,23]. Its core idea is to get a solution of the original equation as a limit of approximations obtained suitably merging S and Σ.…”

Hyperbolic balance laws with a dissipative non local source

“…It is well known that this dissipativity condition allows to prove the well posedness globally in time of the Cauchy problem for (1.1)-(1.2) in the case Q = 0 and g: R n → R n , see [2,14]. Similar global results can be obtained by means of suitable L 1 estimates for relevant classes of systems, see [13].…”

“…It is known, see [11,Theorem 2.1], that for small times equation (1.1) generates a Lipschitz semigroup. When the source term is dissipative, the existence of solutions can be proved for all times, see [13,14] as well as the continuous dependence, see [2,8]. These papers all deal with local sources.…”

Global Existence of Large BV Solutions in a Model of Granular Flow

“…Even in the general case of systems which are neither genuinely nonlinear nor linearly degenerate, global solutions have been constructed by the Glimm scheme [18,21,23,27], by front tracking approximations [4,5], and by vanishing viscosity approximations [7]. In some special cases, existence and uniqueness of global solutions in the presence of a source term were proved in [16,22,12] and in [2,15,1,13,14], respectively.…”