Differential and Integral Equations

Generalized solutions of linear partial differential equations with discontinuous coefficients

Nathalie Caroff

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Abstract

In this paper, we consider the Cauchy problem for linear first-order partial differential equations with discontinuous coefficients. We show that, under suitable assumptions, it has a unique continuous solution. Moreover, this solution is stable under perturbation of the coefficients. We also show that this solution can be expressed explicitly by integrating along generalized characteristics.

Article information

Source
Differential Integral Equations Volume 17, Number 5-6 (2004), 653-668.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060353

Mathematical Reviews number (MathSciNet)
MR2054940

Zentralblatt MATH identifier
1174.35326

Subjects
Primary: 35F10: Initial value problems for linear first-order equations
Secondary: 35C15: Integral representations of solutions 35D05

Citation

Caroff, Nathalie. Generalized solutions of linear partial differential equations with discontinuous coefficients. Differential Integral Equations 17 (2004), no. 5-6, 653--668. https://projecteuclid.org/euclid.die/1356060353.


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