The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 15-27
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For mixed type equation $$ Lu\equiv u_{xx}+sgny\cdot |y|^m u_{yy}=0,\: 01\nonumber $$ \noindent in a rectangular domain $\{(x,y)|\quad 0$, where $m,\alpha,\beta$ – defined positive numbers, theorems of existence and uniqueness of the problem solvability with boundary solutions $u(0,y)=u(1,y)$, $u_x(0,y)=u_x(1,y)$, $-\alpha\leq y\leq \beta$; $u(x,\beta)=f(x)$, $u(x,-\alpha)=g(x),$ $0\le x\le 1$ are proved by the method of spectral analysis.
Keywords:
eigenfunctions, spectral analysis.
@article{VSGU_2009_8_a1,
author = {I. P. Egorova},
title = {The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy},
journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
pages = {15--27},
publisher = {mathdoc},
number = {8},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VSGU_2009_8_a1/}
}
TY - JOUR AU - I. P. Egorova TI - The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy JO - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ PY - 2009 SP - 15 EP - 27 IS - 8 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VSGU_2009_8_a1/ LA - ru ID - VSGU_2009_8_a1 ER -
%0 Journal Article %A I. P. Egorova %T The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy %J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ %D 2009 %P 15-27 %N 8 %I mathdoc %U http://geodesic.mathdoc.fr/item/VSGU_2009_8_a1/ %G ru %F VSGU_2009_8_a1
I. P. Egorova. The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 15-27. http://geodesic.mathdoc.fr/item/VSGU_2009_8_a1/