Boundary value problems and eigenvalue problems for second order equations with nonnegative characteristic Form

1987 ◽  
Vol 12 (12) ◽  
pp. 849-853
Author(s):  
Okumura Hirozo
Keyword(s):  
Boundary Value Problems ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Second Order ◽  
Characteristic Form ◽  
Nonnegative Characteristic Form ◽  
Second Order Equations

scholarly journals Boundary value problems for singular second order equations

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Alessandro Calamai ◽  
Cristina Marcelli ◽  
Francesca Papalini
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Second Order Equations

Numerical methods for the solution of special and general sixth-order boundary-value problems, with applications to Bénard layer eigenvalue problems

1990 ◽  
Vol 431 (1883) ◽  
pp. 433-450 ◽  
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Second Order ◽  
Sixth Order ◽  
Asymptotic Estimates ◽  
Eighth Order ◽  
The Family ◽  
Convergent Method

A family of numerical methods is developed for the solution of special nonlinear sixth-order boundary-value problems. Methods with second-, fourth-, sixth- and eighth-order convergence are contained in the family. The problem is also solved by writing the sixth-order differential equation as a system of three second-order differential equations. A family of second- and fourth-order convergent methods is then used to obtain the solution. A second-order convergent method is discussed for the numerical solution of general nonlinear sixth-order boundary-value problems. This method, with modifications where necessary, is applied to the sixth-order eigenvalue problems associated with the onset of instability in a Bénard layer. Numerical results are compared with asymptotic estimates appearing in the literature.

scholarly journals The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

2016 ◽  
Vol 30 (1) ◽  
pp. 203-217
Author(s):  
Damian Wiśniewski
Keyword(s):  
Weak Solution ◽  
Boundary Value Problems ◽  
Weak Solutions ◽  
Boundary Value ◽  
Continuity Condition ◽  
Second Order ◽  
Second Order Equations ◽  
Elliptic Divergence

AbstractWe investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.

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