Boundary value problems for second order systems in a polyhedral cone

2010 ◽  
pp. 289-353
Author(s):  
Vladimir Maz′ya ◽  
Jürgen Rossmann
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Polyhedral Cone ◽  
Second Order Systems

scholarly journals On Mixed Problems for Quasilinear Second-Order Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Rita Cavazzoni
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Iteration Scheme ◽  
Second Order ◽  
Linear Operators ◽  
Initial Boundary Value Problems ◽  
Mixed Problems ◽  
Second Order Systems ◽  
Initial Boundary Value

The paper is devoted to the study of initial-boundary value problems for quasilinear second-order systems. Existence and uniqueness of the solution in the space , with , is proved in the case where is a half-space of . The proof of the main theorem relies on two preliminary results: existence of the solution to mixed problems for linear second-order systems with smooth coefficients, and existence of the solution to initial-boundary value problems for linear second-order operators whose coefficients depend on the variables and through a function . By means of the results proved for linear operators, the well posedness of the mixed problem for the quasi-linear system is established by studying the convergence of a suitable iteration scheme.

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