Removable singularities on the boundary and uniqueness of solutions of boundary-value problems for second-order elliptic and parabolic equations

1978 ◽  
Vol 11 (3) ◽  
pp. 206-217 ◽  
Author(s):  
O. A. Oleinik ◽  
G. A. Iosif'yan
Keyword(s):  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Removable Singularities ◽  
Elliptic And Parabolic Equations

On corner singularities of solutions to mixed boundary-value problems for second-order elliptic and parabolic equations

1991 ◽  
Vol 433 (1887) ◽  
pp. 209-217 ◽  
Keyword(s):  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Corner Singularities ◽  
Mixed Boundary Value Problems ◽  
Decomposition Formula ◽  
Elliptic And Parabolic Equations ◽  
Time Dependent Problems

In this paper we prove a decomposition formula for solutions of mixed boundary-value problems for elliptic and parabolic equations into regular and singular parts, which provides an explicit description of the behaviour of the solution near the corners of the boundary and also, in parabolic cases, shows how the singularity due to the corners varies in time. We also give some sufficient conditions for the regularity of the solution of time-dependent problems.

scholarly journals On Solution of Two-Point Fuzzy Boundary Value Problems

2014 ◽  
Vol 11 ◽  
pp. 31-39 ◽  
Author(s):  
Hülya Gültekin ◽  
Nihat Altinişik
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Fuzzy Boundary Value Problems ◽  
Fuzzy Boundary

In this paper, we investigate the existence and uniqueness of solutions of two-point fuzzy boundary value problems for second-order fuzzy differential equations. Some sufficient conditions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara differentiability.

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