By N. E. Tovmasyan, L. Z. Gevorkyan, G. V. Zakaryan

ISBN-10: 9810213514

ISBN-13: 9789810213510

This article is dedicated to boundary worth difficulties for common partial differential equations. It develops effective tools of answer of boundary price difficulties for elliptic equations, in line with the speculation of analytic capabilities, having nice theoretical and useful value. a brand new method of the research of electromagnetic fields is sketched, allowing legislation of propagation of electromagnetic strength at a good distance to be defined and asymptotic formulae for ideas of Maxwell's equation to be bought. those equations also are utilized to the effective solution of difficulties.

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**Example text**

X ^) . 1, vector the homogeneous J V ( t ) are problem linearly function vector o f c l a s s M. 99) implies 1 that the independent. ) i s proved. 3. L e t n = l and L o p a t i n s k y ' s c o n d i t i o n be numbers o f p o i n t s f ( J - 1 , 2 , . . ) . rank We shall prove that . 7) i n the class h a s i n f i n i t e number o f l i n e a r l y i n d e p e n d e n t s o l u t i o n s . j)« • 0. 101) 0- ( 1 . 102) J o f v e c t o r a a r e complex numbers. 70), b system y . 72) solutions.

73) Similarly, + c 5ffi J_ — f=£; 2 as : *(t )-Jt(t )-tr(t ), t o (

3) existence of the solution. on x dependinq t h e boundary and conditions shall t only. 13) B 8B 2 (x,tj SB — {X,t) =°< — 3 =°< f - (x,0)=C , SB BE {x,t) (x,t) 3E ( x , t ) ax at ' BJx,Q)=f aB (x,t) at The solution of defined (3-17) a , E J x , 0)=gjx) t h e problem . t), ax (x) , EJx,0)=£Jx) i 4 (x,t) SB = at 1 (3 . 15) 0 is (cf. is) y . 19) i s sought at £>0 ( 3 . 13) and ( 3 . 20) EJx,t)=

### Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics by N. E. Tovmasyan, L. Z. Gevorkyan, G. V. Zakaryan

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