Download Boundary Value Problems for Partial Differential Equations by N. E. Tovmasyan, L. Z. Gevorkyan, G. V. Zakaryan PDF
By N. E. Tovmasyan, L. Z. Gevorkyan, G. V. Zakaryan
This article is dedicated to boundary worth difficulties for basic partial differential equations. It develops effective tools of solution of boundary worth difficulties for elliptic equations, in accordance with the speculation of analytic features, having nice theoretical and sensible value. a brand new method of the research of electromagnetic fields is sketched, allowing legislation of propagation of electromagnetic power at an outstanding distance to be defined and asymptotic formulae for options of Maxwell's equation to be received. those equations also are utilized to the effective solution of difficulties.
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Additional info for Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics
6 6 ) : f f zeD*, t s r . 50). 1) and applying ( 2 . 3 ) we o b t a i n . f K(C , t ) < p ( t ) d t (a+ f i c r v v M V + ~ ^ f t c = < „' - V r - 2 4 ! - ' t where E i s i d e n t i t y m a t r i x o f o r d e r n. 5, r where found, |K(t) = (^ ( t ) ,. , ^ ( 1 ) ) l defined on i s n-dimensional t h e contour T, 30 v e c t o r - f u n c t i o n t o be t h e elements o f which satisfy Holder's condition. 5) t h e v e c t o r - f u n c t i o n of Holder, o f any a n a l y t i c ( 2 . 5 ) i s due t o t h e f a c t p i s an a r b i t r a r y i .
69) . 1) . 59) equation j (£+ i ( t , £ ) ) ( H t ) - X ( t ) ) K p o 0 t o equation ( 2 . 2). 74) r to the Sokhotzky-Plemelj's 1 limit at z^t sr, o zeD* in (2,74) and applying f o r m u l a , we o b t a i n : , i 44 f K(t t) ( (t)-X(t))dt V ! , . 73) Similarly, + c 5ffi J_ — f=£; 2 as : *(t )-Jt(t )-tr(t ), t o (
17). 17) . 25) 1 gej? 26) by: the branch satisfying the conditions: / B -iaf 2 I m / B*-4af From e q u a t i o n s ( 3 . 29) >0 a t e <4a£. 17) 1 . 1 ) . 17) 2 with the order of regularity I t is satisfies o f Theorem solvable 52 that: ReA (0)=0. 2). 1) t h e i s proved. 3,2. 1. The f u n c t i o n f ( x ) belongs t o t h e c l a s s C^(R'), i f i t infinitely differentiable in R and i s equal t o zero outside o fa segment. 19) C™(R') . 8 when o f electromagnetic f i e l d a t t h e great values o f t .