In this paper we establish the existence and uniqueness of the weak solution of a Cauchy problem associated to a conservation law in several space variables, whose non-homogeneous term is a "memory" term. The existence is obtained, in a particular case, by proving the uniform boundedness of the approximating solutions in the BV - norm, and then applying the relative compacteness framework, in the general case, in the L1 framework. The uniqueness is obtained by means of a suitable modification of Kružkov's method .
|Titolo:||Weak Solutions of a conservation law with memory in several space variables|
SAMPALMIERI, ROSELLA COLOMBA (Corresponding)
|Data di pubblicazione:||1998|
|Appare nelle tipologie:||1.1 Articolo in rivista|