scholarly journals On One Approach of Investigation of the Boundary Value Problem for a Quasilinear Hyperbolic Type Equation with Discontinuities in the Right Hand – Side

2019 ◽  
pp. 71-77
Author(s):  
V. V. Marynets ◽  
◽  
O. I. Kogutych ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Type Equation ◽  
Hyperbolic Type ◽  
Right Hand ◽  
The Right

A Method for the Numerical Solution of a Boundary Value Problem for a Linear Differential Equation with Interval Parameters

2019 ◽  
Vol 16 (07) ◽  
pp. 1850115 ◽  
Author(s):  
Nizami A. Gasilov ◽  
Müjdat Kaya
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Linear Differential Equation ◽  
Numerical Method ◽  
Boundary Value ◽  
Real Life ◽  
Boundary Values ◽  
Right Hand ◽  
Linear Differential ◽  
The Right

In many real life applications, the behavior of the system is modeled by a boundary value problem (BVP) for a linear differential equation. If the uncertainties in the boundary values, the right-hand side function and the coefficient functions are to be taken into account, then in many cases an interval boundary value problem (IBVP) arises. In this study, for such an IBVP, we propose a different approach than the ones in common use. In the investigated IBVP, the boundary values are intervals. In addition, we model the right-hand side and coefficient functions as bunches of real functions. Then, we seek the solution of the problem as a bunch of functions. We interpret the IBVP as a set of classical BVPs. Such a classical BVP is constructed by taking a real number from each boundary interval, and a real function from each bunch. We define the bunch consisting of the solutions of all the classical BVPs to be the solution of the IBVP. In this context, we develop a numerical method to obtain the solution. We reduce the complexity of the method from [Formula: see text] to [Formula: see text] through our analysis. We demonstrate the effectiveness of the proposed approach and the numerical method by test examples.

On a fractional differential inclusion with “maxima”

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Aurelian Cernea
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Differential Inclusion ◽  
Right Hand ◽  
Fractional Differential ◽  
The Right

Abstract We study a boundary value problem associated to a fractional differential inclusion with “maxima”. Several existence results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

scholarly journals New fixed point approach for a fully nonlinear fourth order boundary value problem

2018 ◽  
Vol 36 (4) ◽  
pp. 209-223 ◽  
Author(s):  
Dang Quang A ◽  
Ngo Thi Kim Quy
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Linear Growth ◽  
Boundary Value ◽  
Iterative Solution ◽  
Fixed Point Approach ◽  
Right Hand ◽  
The Right ◽  
Uniqueness Of A Solution ◽  
Theoretical Results

In this paper we propose a method for investigating the solvability and iterative solution of a nonlinear fully fourth order boundary value problem. Namely, by the reduction of the problem to an operator equation for the right-hand side function we establish the existence and uniqueness of a solution and the convergence of an iterative process. Our method completely differs from the methods of other authors and does not require the condition of boundedness or linear growth of the right-hand side function on infinity. Many examples, where exact solutions of the problems are known or not, demonstrate the effectiveness of the obtained theoretical results.

scholarly journals On Neumann problem for the degenerate Monge–Ampère type equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Juhua Shi ◽  
Feida Jiang
Keyword(s):  
Neumann Problem ◽  
Viscosity Solution ◽  
Boundary Value ◽  
Type Equation ◽  
Neumann Boundary ◽  
Boundary Value Condition ◽  
Right Hand ◽  
The Matrix ◽  
The Right ◽  
Monge Ampere

AbstractIn this paper, we study the global $C^{1, 1}$ C 1 , 1 regularity for viscosity solution of the degenerate Monge–Ampère type equation $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) with the Neumann boundary value condition $D_{\nu }u=\varphi (x)$ D ν u = φ ( x ) , where the matrix A is under the regular condition and some structure conditions, and the right-hand term B is nonnegative.

scholarly journals On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain

2020 ◽  
Vol 24 (2) ◽  
pp. 211-225
Author(s):  
Zhiraslan Anatolievich Balkizov
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Type Equation ◽  
Hyperbolic Type ◽  
Displacement Boundary Condition ◽  
Third Order ◽  
Displacement Boundary

Исследована краевая задача со смещением для неоднородного уравнения параболо-гиперболического типа третьего порядка с волновым оператором в области гиперболичности, когда в качестве одного из граничных условий задана линейная комбинация с переменными коэффициентами производных от значений искомой функции на независимых характеристиках, а также на линии изменения типа и порядка. Найдены необходимые и достаточные условия существования и единственности регулярного решения задачи. В некоторых частных случаях представление решения исследуемой задачи выписано в явном виде.

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