Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Qualitative behavior of conservation laws with reaction term and nonconvex flux

Author: Corrado Mascia
Journal: Quart. Appl. Math. 58 (2000), 739-761
MSC: Primary 35L65; Secondary 35L60, 74J30
DOI: https://doi.org/10.1090/qam/1788426
MathSciNet review: MR1788426
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Abstract: The aim of the paper is to study qualitative behavior of solutions to the equation

$\displaystyle \frac{{\partial u}}{{\partial t}} + \frac{{\partial f\left( u \right)}}{{\partial x}} = g\left( u \right) ,$

where $ \left( x, t \right) \in \mathbb{R} \times {\mathbb{R}_ + }, u = u\left( x, t \right) \in \mathbb{R}$. The main new feature with respect to previous works is that the flux function $ f$ may have finitely many inflection points, intervals in which it is affine, and corner points. The function $ g$ is supposed to be zero at 0 and 1, and positive in between.

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DOI: https://doi.org/10.1090/qam/1788426
Article copyright: © Copyright 2000 American Mathematical Society

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