The Mapping of the Main Functions and Different Variations of YH-DIE

2020 ◽  
Author(s):  
Gilbert Mason ◽  
Yuanjue Chou ◽  
Springer Pind
Keyword(s):  
Algebraic Geometry ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Minimal Surface ◽  
Access Point ◽  
Partial Differential ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Fusion Point ◽  
Special Case

YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.

ON TAYLOR'S SCRAPING PROBLEM AND FLOW OF A SISKO FLUID

2009 ◽  
Vol 14 (4) ◽  
pp. 515-529 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Ali R. Ansari ◽  
Ahmed Ahmad ◽  
N. Ahmad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Normal Stress ◽  
Partial Differential ◽  
Sisko Fluid ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Special Case

The aim of the present investigation is to study the properties of a Sisko fluid flowing between two intersecting planes. The problem is similar to Taylor's scraping problem for a viscous fluid. We determine the solution of the complicated set of non‐linear partial differential equations describing the flow analytically. The analysis is carried out in detail reflecting the effects of varying the angle of the scraper on the flow. In addition, the tangential and normal stress are also computed. We also show the well known Taylor scraper problem as a special case.

Higher-order estimates for fully nonlinear difference equations. I

2000 ◽  
Vol 43 (3) ◽  
pp. 485-510 ◽  
Author(s):  
Derek W. Holtby
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Equations ◽  
A Priori ◽  
Elliptic Partial Differential Equations ◽  
Uniform Mesh ◽  
Partial Differential ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Special Case

AbstractThe purpose of this work is to establish a priori C2, α estimates for mesh function solutions of nonlinear positive difference equations in fully nonlinear form on a uniform mesh, where the fully nonlinear finite-difference operator ℱh is concave in the second-order variables. The estimate is an analogue of the corresponding estimate for solutions of concave fully nonlinear elliptic partial differential equations. We deal here with the special case that the operator does not depend explicitly upon the independent variables. We do this by discretizing the approach of Evans for fully nonlinear elliptic partial differential equations using the discrete linear theory of Kuo and Trudinger. The result in this special case forms the basis for a more general result in part II. We also derive the discrete interpolation inequalities needed to obtain estimates for the interior C2, α semi-norm in terms of the C0 norm.

scholarly journals Nonlinearly Self-Adjoint, Conservation Laws and Solutions for a Forced BBM Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Maria Luz Gandarias ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
General Theorem ◽  
Partial Differential ◽  
Symmetry Generators ◽  
Special Case ◽  
Bbm Equation

We study a forced Benjamin-Bona-Mahony (BBM) equation. We prove that the equation is not weak self-adjoint; however, it is nonlinearly self-adjoint. By using a general theorem on conservation laws due to Nail Ibragimov and the symmetry generators, we find conservation laws for these partial differential equations without classical Lagrangians. We also present some exact solutions for a special case of the equation.

scholarly journals Ideals Generated by Differential Equations

2020 ◽  
pp. 170-186
Author(s):  
OlegV. Kaptsov
Keyword(s):  
Algebraic Geometry ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential System ◽  
Commutative Algebra ◽  
Algebraic Approach ◽  
Jet Space ◽  
Passive Systems ◽  
Partial Differential ◽  
Condi Tions

We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gr¨obner bases to clarify crucial notions concerning compatibility such as passivity and reducibility. One obtains sufficient condi- tions for a differential system to be passive and proves that such systems generate manifolds in the jet space. Some examples of constructions of passive systems associated with the sinh-Cordon equation are given

scholarly journals Approximation of partial differential equations on compact resistance spaces

2021 ◽  
Vol 61 (1) ◽  
Author(s):  
Michael Hinz ◽  
Melissa Meinert
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Quadratic Forms ◽  
Main Interest ◽  
Partial Differential ◽  
Metric Graph ◽  
Linear Partial Differential Equations ◽  
Accumulation Points ◽  
Solutions Of Equations ◽  
Special Case

AbstractWe consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and divergence terms. Our main interest is to provide graph and metric graph approximations for their unique solutions. For families of equations with different coefficients on a single compact resistance space we prove that solutions have accumulation points with respect to the uniform convergence in space, provided that the coefficients remain bounded. If in a sequence of equations the coefficients converge suitably, the solutions converge uniformly along a subsequence. For the special case of local resistance forms on finitely ramified sets we also consider sequences of resistance spaces approximating the finitely ramified set from within. Under suitable assumptions on the coefficients (extensions of) linearizations of the solutions of equations on the approximating spaces accumulate or even converge uniformly along a subsequence to the solution of the target equation on the finitely ramified set. The results cover discrete and metric graph approximations, and both are discussed.

scholarly journals A duality result between the minimal surface equation and the maximal surface equation

2001 ◽  
Vol 73 (2) ◽  
pp. 161-164 ◽  
Author(s):  
LUIS J. ALÍAS ◽  
BENNETT PALMER
Keyword(s):  
Euclidean Space ◽  
Differential Equations ◽  
Minimal Surface ◽  
Minkowski Space ◽  
Minimal Surfaces ◽  
Maximal Surface ◽  
Maximal Surfaces ◽  
Surface Equation ◽  
Duality Result ◽  
Minimal Surface Equation

In this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's theorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa). This follows from a simple but nice duality between solutions to their corresponding differential equations.

scholarly journals A Parabolic Transform and Averaging Methods for General Partial Differential Equations

2019 ◽  
Vol 17 ◽  
pp. 352-361
Author(s):  
Mahmoud Mohammed Mostafa El-Borai ◽  
Hamed Kamal Awad Awad ◽  
Randa Hamdy. M. Ali Ali
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Operators ◽  
Averaging Method ◽  
Partial Differential ◽  
Averaging Methods ◽  
Partial Differential Operators ◽  
Existence And Stability ◽  
Special Case ◽  
Stability Results

Averaging method of the fractional general partial differential equations and a special case of these equations are studied, without any restrictions on the characteristic forms of the partial differential operators. We use the parabolic transform, existence and stability results can be obtained.

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