Thoughts on the Busemann equation
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A second-order quasi-linear partial differential equation of mixed elliptic-hyperbolic type in two independent variables, which mimics one introduced by A. Busemann in gas dynamics, and arises in the study of Minkowski spaces and in other theories, is considered.
Mathematics Subject Classification (2010)Primary 35M10 35M11 35Q35 35Q60 Secondary 35D40 35F50
KeywordsSecond-order quasi-linear partial differential equations of mixed type first-order non-linear partial differential systems Bäcklund transformations complex-valued eikonals minimal surfaces space-like maximal surfaces in Minkowski space Legendre transformation Lavrentiev-Bitsadze equation D’Alembert equation initial value problems
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