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Uniqueness of Entropy Solutions
2002In this chapter, we establish a general uniqueness theorem for nonlinear hyperbolic systems. Solutions are sought in the space of functions with bounded variation, slightly restricted by the so-called tame variation condition (Definition 1.1). The results of existence and continuous dependence established in previous chapters covered solutions obtained
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Existence and Uniqueness of Solutions
1992Recall the inhomogeneous system (I) of k linear equations in n unknowns, which we studied in Chapter 4.4. We consider the case k = n, where the number of equations to be solved equals the number of unknowns, and we shall use our results about bases in ℝ n in the preceding chapter to study the question of existence and uniqueness of solutions of the ...
Thomas Banchoff, John Wermer
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Uniqueness of Viscosity Solutions
2016We shall present the uniqueness proof, originally due to Jensen, Arch Ration Mechan Anal 123:51–74, 1993 [J], for the Dirichlet problem in a bounded, but otherwise quite arbitrary domain.
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Existence and Uniqueness of Solutions
1968In Chapter 6 we have repeatedly postponed an investigation of the existence and uniqueness of the current chains and voltage chains describing the performance of a resistive network, but subject to the restrictions imposed by Ohm’s Law and Kirchhoff’s Current and Voltage Laws. In the first part of this Chapter we finally consider such matters.
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Existence and Uniqueness of Solutions
2009A fundamental issue in the theory of differential equations consists of proving the existence and uniqueness of solutions. Before we discuss partial differential equations, we analyse in Section 9.1 the situation for general systems of ordinary differential equations, often called differential algebraic equations.
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