For the Riemann problem {u(t) + (Phi (u, x))(x) = 0, u vertical bar(t=0) = u_ + [u]theta(x) a new definition of the solution is proposed. We associate a Hamiltonian system with initial conservation law, and define the geometric solution as the result of the action of the phase flow on the initial curve. In the second part of this paper, we construct the equalization procedure, which allows us to juxtapose a geometric solution with a unique entropy solution under the condition that Phi does not depend on x. If Phi depends on x, then the equalization procedure allows us to construct a generalized solution of the original Riemann problem.
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Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Hinohara, Kihito
Minagawa, Natsuki
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Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Minagawa, Natsuki
Ohwa, Hiroki
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Niigata Univ, Fac Sci, Dept Math, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Ohwa, Hiroki
Suzuki, Hiroya
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Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Suzuki, Hiroya
Ukita, Shou
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Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
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Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Yuan, Qian
Yuan, Yuan
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South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou, Guangdong, Peoples R China
Univ Brescia, Sez Matemat, DICATAM, Via Valotti 9, I-25133 Brescia, ItalyChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
机构:
Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Hinohara, Kihito
Minagawa, Natsuki
论文数: 0引用数: 0
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机构:
Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Minagawa, Natsuki
Ohwa, Hiroki
论文数: 0引用数: 0
h-index: 0
机构:
Niigata Univ, Fac Sci, Dept Math, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Ohwa, Hiroki
Suzuki, Hiroya
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h-index: 0
机构:
Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
Suzuki, Hiroya
Ukita, Shou
论文数: 0引用数: 0
h-index: 0
机构:
Niigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, JapanNiigata Univ, Grad Sch Sci & Technol, Nishi Ku, 8050 Ikarashi 2 No Cho, Niigata 9502181, Japan
机构:
Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Yuan, Qian
Yuan, Yuan
论文数: 0引用数: 0
h-index: 0
机构:
South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou, Guangdong, Peoples R China
Univ Brescia, Sez Matemat, DICATAM, Via Valotti 9, I-25133 Brescia, ItalyChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China