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Zapiski Nauchnykh Seminarov POMI, 1996, Volume 233, Pages 30–52
(Mi znsl3659)
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This article is cited in 3 scientific papers (total in 3 papers)
On a construction of weak solutions to linear hyperbolic partial differential systems with the higher integrable gradients
K. Hoshino, N. Kikuchi Keio University, Japan
Abstract:
By taking linear hyperbolic partial differential equations as an illustration, we make a trial of constructing weak solutions, with the higher integrable gradients in the sense of Gehring, to hyperbolic differential equations with initial and boundary conditions. We adopt Rothe's method and follow the calculation which has been expanded by Giaquinta and Struwe in dealing with parabolic equations. To establish the scheme we evaluate some local estimates for solutions to Rothe's approximations to hyperbolic differential equations. Bibl. 6 titles.
Received: 20.09.1995
Citation:
K. Hoshino, N. Kikuchi, “On a construction of weak solutions to linear hyperbolic partial differential systems with the higher integrable gradients”, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Zap. Nauchn. Sem. POMI, 233, POMI, St. Petersburg, 1996, 30–52; J. Math. Sci. (New York), 93:5 (1999), 636–652
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https://www.mathnet.ru/eng/znsl3659 https://www.mathnet.ru/eng/znsl/v233/p30
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Abstract page: | 84 | Full-text PDF : | 54 |
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