Regularity Estimates for Nondivergence Parabolic Equations on Generalized Orlicz Spaces

2020 ◽  
Author(s):  
The Anh Bui
Keyword(s):  
Parabolic Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Harmonic Analysis ◽  
Parabolic Equations ◽  
Orlicz Spaces ◽  
Representation Theorems ◽  
New Approach ◽  
Analysis Techniques ◽  
Regularity Estimates

Abstract In this paper, by using a new approach, we prove regularity estimates for the solution to the nondivergence parabolic equation on generalized Orlicz spaces. Our approach can be viewed as a combination of representation theorems in partial differential equations and harmonic analysis techniques.

A New Approach to Teaching Thermofluids Dimensional Analysis

2000 ◽  
Vol 28 (2) ◽  
pp. 174-184 ◽  
Author(s):  
Mark R. D. Davies ◽  
Tara M. Dalton
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dimensional Analysis ◽  
New Approach ◽  
Flow And Heat Transfer ◽  
Single Method ◽  
Approach To Teaching ◽  
Simple Equations

A new method of dimensional analysis is presented by demonstrating its application to a range of problems in fluid flow and heat transfer. The technique is a development of a previously published and accepted method of inspectional analysis. This new technique is shown to give the correct results on both simple equations with solutions, and on more complex sets of partial differential equations without solutions. This development of a single method from the simple to the complex has obvious teaching advantages.

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