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1997 First-order partial differential equations and Henstock-Kurzweil integrals
Tuan Seng Chew, B. Van-Brunt, G. C. Wake
Differential Integral Equations 10(5): 947-960 (1997). DOI: 10.57262/die/1367438627


The existence and uniqueness of solutions to the Cauchy problem for a first-order quasi-linear partial differential equation is studied in this paper using the Henstock-Kurzweil integral. The classical theory requires certain differentiability and continuity conditions on the coefficients of the derivatives in the equation. It is shown here that in the Henstock-Kurzweil integral setting these conditions can be relaxed and that the resulting solution is differentiable though the derivatives need not be continuous. This sharpens the classical result and provides a bridge between classical and weak solutions in the linear case.


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Tuan Seng Chew. B. Van-Brunt. G. C. Wake. "First-order partial differential equations and Henstock-Kurzweil integrals." Differential Integral Equations 10 (5) 947 - 960, 1997.


Published: 1997
First available in Project Euclid: 1 May 2013

zbMATH: 0890.35025
MathSciNet: MR1741760
Digital Object Identifier: 10.57262/die/1367438627

Primary: 35F25
Secondary: 26A39

Rights: Copyright © 1997 Khayyam Publishing, Inc.


Vol.10 • No. 5 • 1997
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