On the solution of a boundary-value problem for a third-order equation with multiple characteristics

2012 ◽  
Vol 64 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Yu. P. Apakov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Order Equation ◽  
Third Order ◽  
Multiple Characteristics

scholarly journals Boundary value problem with integral conditions for a linear third-order equation

2003 ◽  
Vol 2003 (11) ◽  
pp. 553-567 ◽  
Author(s):  
M. Denche ◽  
A. Memou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Order Equation ◽  
Integral Conditions ◽  
Third Order ◽  
Integral Boundary

We prove the existence and uniqueness of a strong solution for a linear third-order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.

ON THE SOLUTIONS OF NONLINEAR THIRD ORDER BOUNDARY VALUE PROBLEMS

2010 ◽  
Vol 15 (1) ◽  
pp. 127-136
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Order Equation ◽  
Structure Of Solutions ◽  
Third Order ◽  
Number Of Solutions ◽  
The Third

The author considers a three‐point third order boundary value problem. Properties and the structure of solutions of the third order equation are discussed. Also, a connection between the number of solutions of the boundary value problem and the structure of solutions of the equation is established.

scholarly journals A PRIORI ESTIMATION OF A GENERALIZED NONLOCAL BOUNDARY VALUE PROBLEM FOR A THRID ORDER EQUATION WITH A FRACTIONAL TIME CAPUTO DERIVATIVE

2019 ◽  
pp. 35-40
Author(s):  
А.М. Шхагапсоев
Keyword(s):  
Boundary Value Problem ◽  
Caputo Derivative ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Fractional Caputo Derivative ◽  
Multiple Characteristics ◽  
A Priori Estimation

Рассматривается краевая задача для уравнения третьего порядка параболического типа с дробной производной Капуто. Методом энергетических неравенств получена априорная оценка решения обобщенной нелокальной краевой задачи для уравнения с кратными характеристиками с дробной производной Капуто по времени. A boundary value problem for a third-order parabolic equation with a fractional Caputo derivative is considered. A priori estimation of the solution of a generalized nonlocal boundary value problem for an equation with multiple characteristics with a fractional Caputo derivative in time is obtained by the method of energy inequalities.

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