Publication: Renormalized entropy solutions of scalar conservation laws.
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2002
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Scuola Normale Superiore
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Abstract
A scalar conservation law ut +div (u) = f is considered with the initial datum u|t=0 = u0 2 L1 loc(RN) and f 2 L1
loc(RN ×(0, T)) only. In this case the classical Krushkov condition can make no sense because of unboundedness of u, if no growth condition on is assumed. This obstacle
is overcome by introducing the so-called renormalized entropy solution generalizing the classical one. Existence and uniqueness of such a solution is established.
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