tailieunhanh - Báo cáo hóa học: " Research Article Two-Dimension Riemann Initial-Boundary Value Problem of Scalar Conservation Laws with Curved Boundary"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Two-Dimension Riemann Initial-Boundary Value Problem of Scalar Conservation Laws with Curved Boundary | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 138396 16 pages doi 2011 138396 Research Article Two-Dimension Riemann Initial-Boundary Value Problem of Scalar Conservation Laws with Curved Boundary Huazhou Chen1 2 and Tao Pan2 1 Department of Mathematics Shanghai University Shanghai 200444 China 2 Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Educational Institutes Jinan University Guangzhou 510632 China Correspondence should be addressed to Tao Pan tpan@ Received 16 December 2010 Accepted 1 February 2011 Academic Editor Julio Rossi Copyright 2011 H. Chen and T. Pan. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. This paper is concerned with the structure of the weak entropy solutions to two-dimension Riemann initial-boundary value problem with curved boundary. Firstly according to the definition of weak entropy solution in the sense of Bardos-Leroux-Nedelec 1979 the necessary and sufficient condition of the weak entropy solutions with piecewise smooth is given. The boundary entropy condition and its equivalent formula are proposed. Based on Riemann initial value problem weak entropy solutions of Riemann initial-boundary value problem are constructed the behaviors of solutions are clarified and we focus on verifying that the solutions satisfy the boundary entropy condition. For different Riemann initial-boundary value data there are a total of five different behaviors of weak entropy solutions. Finally a worked-out specific example is given. 1. Introduction Multidimensional conservation laws are a famous hard problem that plays an important role in mechanics and physics 1-3 . For Cauchy problem of multi-dimensional scalar conservation laws Conway and Smoller 4 and Kruzkov 1 have proved that weak solution uniquely

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