scholarly journals GENERALIZATION OF RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR A FIRST ORDER NONLINEAR COMPLEX PARTIAL DIFFERENTIAL EQUATION

2016 ◽  
Vol 29 (1) ◽  
Author(s):  
N. Taghizadeh ◽  
H. Hoseini
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Partial Differential ◽  
First Order ◽  
Hilbert Boundary Value Problem

scholarly journals A note on the nonlocal boundary value problem for a third order partial differential equation

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 801-808 ◽  
Author(s):  
Kh. Belakroum ◽  
A. Ashyralyev ◽  
A. Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Order Partial Differential Equation ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.

scholarly journals A segmented Adomian algorithm for the boundary value problem of a second-order partial differential equation on a plane triangle area

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yin-shan Yun ◽  
Ying Wen ◽  
Temuer Chaolu ◽  
Randolph Rach
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Groundwater Flow ◽  
Boundary Value ◽  
Flow Region ◽  
Second Order ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Adomian Decomposition

Abstract For the boundary value problem (BVP) of a second-order partial differential equation on a plane triangle area, we propose a new algorithm based on the Adomian decomposition method (ADM) combined with a segmented technique. In addition, we present a new theorem that ensures the convergence of the algorithm. By this algorithm, the model for the effect of regional recharge on the plane triangle groundwater flow region is solved, from which we obtain the segmented exact solution of the problem, which satisfies the governing equation and all of the specified boundary conditions. Then, by the algorithm combined with Taylor’s formula, the heterogeneous aquifer model on the plane triangle groundwater flow region is considered, from which we obtain the segmented high-precision approximate solution of the problem.

scholarly journals Comparison results for nonlinear divergence structure elliptic PDE’s

2019 ◽  
Vol 9 (1) ◽  
pp. 438-448 ◽  
Author(s):  
Yichen Liu ◽  
Monica Marras ◽  
Giovanni Porru
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Comparison Result ◽  
Partial Differential ◽  
Laplace Equations ◽  
Comparison Results ◽  
Divergence Structure

Abstract First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.

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