Local estimates of solutions of the stationary two-dimensional first boundary-value problem of magnetohydrodynamics

1996 ◽  
Vol 48 (8) ◽  
pp. 1171-1181
Author(s):  
N. A. Britov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
Estimates Of Solutions

On the solution to a two-dimensional boundary value problem of heat conduction in a degenerating domain

2020 ◽  
Vol 98 (2) ◽  
pp. 100-109
Author(s):  
Minzilya T. Kosmakova ◽  
◽  
Valery G. Romanovski ◽  
Dana M. Akhmanova ◽  
Zhanar M. Tuleutaeva ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
Dimensional Boundary

On the existence and ‘blow-up’ of solutions to a two-dimensional nonlinear boundary-value problem arising in corrosion modelling

2003 ◽  
Vol 133 (1) ◽  
pp. 119-149 ◽  
Author(s):  
Otared Kavian ◽  
Michael Vogelius
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Finite Number ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Boundary Value ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Limiting Behaviour ◽  
Corrosion Modelling

Let Ω be a bounded C2,α domain in R2. We prove that the boundary-value problem Δυ = 0 in Ω, ∂υ/∂n = λsinh(υ) on ∂Ω, has infinitely many (classical) solutions for any given λ > 0. These solutions are constructed by means of a variational principle. We also investigate the limiting behaviour as λ → 0+; indeed, we prove that each of our solutions, as λ → 0+, after passing to a subsequence, develops a finite number of singularities located on ∂Ω.

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