Hyperbolic Conservation Laws with Fading Memory
نویسنده
چکیده
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 type are materials with fading memory that correspond to constitutive relations of the form
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