On the diffraction of an electromagnetic pulse by a wedge

1952 ◽  
Vol 212 (1111) ◽  
pp. 547-551 ◽  
Keyword(s):  
Plane Wave ◽  
Boundary Value Problem ◽  
Potential Theory ◽  
Electromagnetic Pulse ◽  
Boundary Value ◽  
Electromagnetic Disturbance ◽  
Two Dimensional ◽  
Arbitrary Polarization ◽  
Transient Electromagnetic ◽  
Classical Means

The diffraction by a conducting wedge of a transient electromagnetic disturbance in the form of a plane wave discontinuity having arbitrary polarization and direction of propagation is reduced to a pair of two-dimensional scalar problems. The solution to one of these is identical with that previously obtained for the analogous acoustical problem, while the second is attacked in a similar manner, using a Tschplygin transformation to reduce the boundary value problem to one in potential theory, which is then solved by classical means.

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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