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Existence theory and qualitative properties of the solutions of some first order quasilinear variational inequalities.

Díaz Díaz, Jesús Ildefonso and Véron, Laurent (1983) Existence theory and qualitative properties of the solutions of some first order quasilinear variational inequalities. Indiana University Mathematics Journal, 32 (3). pp. 319-361. ISSN 0022-2518

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The authors consider first-order equations in "conservation laws'' form perturbed by a semilinear nonlinearity of monotone type. The known existence and uniqueness results for conservation laws—results due to Kruzhkov—are easily adapted to this situation and some qualitative properties of the solutions are discussed.

Item Type:Article
Uncontrolled Keywords:entropy condition; conservation laws; multivalued operator; comparison principles; finite speed of propagation; Cauchy problem; maximal monotone graph; solution in Kruzkov sense; semigroup solution; compact support
Subjects:Sciences > Mathematics > Differential equations
ID Code:16430

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