An Error Estimate for Viscous Approximate Solutions of Degenerate Parabolic Equations
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چکیده
where QT = R d×(0, T ) with T > 0 fixed, u : QT → R is the sough function, V : R → R is a (not necessarily divergence free) velocity field, f : R → R is the convective flux function, and A : R → R is the “diffusion” function. For the diffusion function the basic assumption is that A(·) is nonincreasing. This condition implies that (1.1) is a (strongly) degenerate parabolic problem. For example, the hyperbolic equation ∂tw + div ( V (x)f(w) ) = 0 is a special case of (1.1). Problems such as (1.1) occur in several important applications. We
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تاریخ انتشار 2007