NDLI: Uniqueness, comparison, and well-posedness results for quasilinear differential equations

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Uniqueness, comparison, and well-posedness results for quasilinear differential equations

Content Provider	Scilit
Author	Carl, S. Heikkila, Seppo
Copyright Year	2000
Description	Chapter 3 Uniqueness, comparison, and well-posedness results for quasilinear dierential equations The purpose of this chapter is to present comparison, uniqueness, and well- posedness results for initial and boundary value problems of rst and second order quasilinear dierential equations. We begin section 3.1 with a com- parison principle, which is then applied to prove comparison and uniqueness results for a boundary value problem of the dierential equation d dt '(t; u(t)) = g(t; u(t)): In section 3.2 we apply an analogous procedure to provide comparison and uniqueness results for initial value problems of the above-mentioned dier- ential equation and the implicit dierential equation d dt '(t; u(t)) = g(t; u(t)) + f(t; u(t); d dt '(t; u(t)) g(t; u(t))): The assumptions imposed on the functions ', g, and f allow them to be discontinuous in all their variables. The so-obtained results, combined with existence results derived in chapter 2, yield also existence and uniqueness results for the above problems with '(t; u(t)) replaced by '(u(t)). Book Name: Nonlinear Differential Equations in Ordered Spaces
Related Links	https://content.taylorfrancis.com/books/download?dac=C2010-0-47957-5&isbn=9780429179617&doi=10.1201/9781482280951-7&format=pdf
DOI	10.1201/9781482280951-7
Language	English
Publisher	Informa UK Limited
Publisher Date	2000-06-14
Access Restriction	Open
Subject Keyword	Book Name: Nonlinear Differential Equations in Ordered Spaces Mathematics Differential Boundary Quasilinear Dierential Equation Equations Chapter Well Posedness Posedness Results
Content Type	Text
Resource Type	Chapter

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