Singular perturbation of first boundary value problem for higher order elliptic equations (II)

1981 ◽  
Vol 2 (5) ◽  
pp. 613-623 ◽  
Author(s):  
Zheng Yong-shu
Keyword(s):  
Singular Perturbation ◽  
Boundary Value Problem ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Higher Order

scholarly journals A Boundary Value Problem for Higher Order Elliptic Equations in Many Connected Domain on the Plane

2017 ◽  
Author(s):  
А.П. Солдатов
Keyword(s):  
Boundary Value Problem ◽  
Connected Domain ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Higher Order

Для эллиптического уравнения $2l$ порядка, старшие коэффициенты которого постоянны, в многосвязной области с гладкой границней на плоскости рассмотрена краевая задача с нормальными производными $(k_j-1)-$ порядка, $j = 1,\ldots,l$, где $1 \le k_1 < \ldots < k_l\le 2l$. При $k_j = j $ она переходит в задачу Дирихле, а при $k_j = j + 1$~--- в задачу Неймана. В работе даны остаточное условие фредгольмовости этой задачи и формула индекса.

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

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