scholarly journals A special case of the normal derivative problem for a third order composite partial differential equation

1954 ◽  
Vol 5 (5) ◽  
pp. 720-720
Author(s):  
Robert B. Davis
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Normal Derivative ◽  
Third Order ◽  
Partial Differential ◽  
Derivative Problem ◽  
Special Case

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 I. On curvature and orthogonal surfaces

1873 ◽  
Vol 21 (139-147) ◽  
pp. 166-167
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Orthogonal System ◽  
The Other ◽  
Third Order ◽  
Partial Differential ◽  
The Third ◽  
The Subject

The principal object of the present Memoir is the establishment of the partial differential equation of the third order satisfied by the parameter of a family of surfaces belonging to a triple orthogonal system. It was first remarked by Bouquet that a given family of surfaces does not in general belong to an orthogonal system, but that (in order to its doing so) a condition must be satisfied: it was afterwards shown by Serret that the condition is that the parameter considered as a function of the coordinates must satisfy a partial differential equation of the third older, this equation was not obtained by him or the other French geometers engaged on the subject, although methods of obtaining it, essentially equivalent but differing in form, were given by Darboux and Levy.

Innovative Derivation for Physics Relations

2013 ◽  
Vol 284-287 ◽  
pp. 478-482
Author(s):  
Hsien Chang Shih ◽  
Huei Jeng Lin
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Specific Area ◽  
Partial Differential ◽  
Physics First ◽  
General Physics ◽  
Future Studies ◽  
Maxwell Relation ◽  
Modern Physics ◽  
Special Case

Classical physics can be regarded as a special case of modern physics. Therefore, we applied those aspects of established modern physics that are suitable for engineering considerations, used the quantum mechanics viewpoint to deal with the physics relations in thermodynamics, and discussed the relations among the variables of physics. We obtained some results by deriving them from basic theories and physics relations, and by exploring the significance of mathematical physics. First, this study obtained the partial differential equation for the general physics relations, which is interesting and revolutionary thinking from the viewpoints of multi-physics and thermodynamic relations expansion. Meanwhile, variable relations among different physics disciplines can be obtained by applying the universal general physics relations with the Jacobian operator. The Maxwell relation is an even more special case; therefore, the physics relations obtained by this study are more universal and versatile. To further illustrate the advantages of this research, the partial differential equation obtained by this study is used to handle the various physics variables and to obtain the thermodynamic physics relations table. This study promotes the research and development of thermodynamic physics relations. There is still room for further exploration in future studies, especially in the specific area of multi-physics application relations and microscopic applications.

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