scholarly journals The asymptotic behavior of solutions of second order systems of partial differential equations

1973 ◽  
Vol 13 (1) ◽  
pp. 57-80 ◽  
Author(s):  
Amy C Murray ◽  
M.H Protter
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Asymptotic Behavior Of Solutions ◽  
Partial Differential ◽  
Second Order Systems

Some second-order systems of partial differential equations of composite type

1987 ◽  
Vol 106 (1-2) ◽  
pp. 73-88 ◽  
Author(s):  
Lin Wei
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Systems ◽  
Second Order ◽  
Cauchy Type ◽  
Linear Transformations ◽  
Partial Differential ◽  
Composite Systems ◽  
Composite Type ◽  
Second Order Systems

SynopsisThe Cauchy problem and the Dirichlet-Cauchy type problem of some second-order systems of partial differential equations of composite type of two unknown functions are investigated. Such systems possess some of the characteristics not only of elliptic but also of hyperbolic systems in the same domain. Representations of the solutions are found for the upper half plane. To this end, the composite systems are reduced to the canonical form by means of successive applications of three kinds of linear transformations. Function theoretic methods are used to obtain representation formulae. Furthermore, some composite systems of 2m-unknown function are also considered.

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