Dissipative and Entropy Solutions to Non-isotropic Degenerate Parabolic Balance Laws
نویسندگان
چکیده
Abstract. We propose a new notion of weak solutions (dissipative solutions) for nonisotropic, degenerate, second order, quasi-linear parabolic equations. This class of solutions is an extension of the notion of dissipative solutions for scalar conservation laws introduced by L. C. Evans. We analyze the relationship between the notions of dissipative and entropy weak solutions for non-isotropic, degenerate, second order, quasi-linear parabolic equations. As an application we prove the strong convergence of a general relaxation–type approximation for such equations.
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