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 [8].
Weak Solutions of a conservation law with memory in several space variables
SAMPALMIERI, ROSELLA COLOMBA
1998-01-01
Abstract
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 [8].File in questo prodotto:
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