Differential and Integral Equations
- Differential Integral Equations
- Volume 17, Number 5-6 (2004), 653-668.
Generalized solutions of linear partial differential equations with discontinuous coefficients
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.
Differential Integral Equations Volume 17, Number 5-6 (2004), 653-668.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35F10: Initial value problems for linear first-order equations
Secondary: 35C15: Integral representations of solutions 35D05
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.