scholarly journals An abstract framework for parabolic PDEs on evolving spaces

2015 ◽  
Vol 72 (1) ◽  
pp. 1-46 ◽  
Author(s):  
Amal Alphonse ◽  
Charles Elliott ◽  
Björn Stinner
Keyword(s):  
Parabolic Pdes ◽  
Abstract Framework

scholarly journals MAPPING AND ENHANCING DESIGN STUDIES WITH PSI META-THEORETIC DESIGN FRAMEWORK

2021 ◽  
Vol 1 ◽  
pp. 2007-2016
Author(s):  
Yoram Reich ◽  
Eswaran Subrahmanian
Keyword(s):  
Design Research ◽  
The Other ◽  
Design Studies ◽  
Abstraction Level ◽  
Follow Up Studies ◽  
The One ◽  
The Right ◽  
Abstract Framework ◽  
Tools And Methods

AbstractDesign research as a field has been studied from diverse perspectives starting from product inception to their disposal. The product of these studies includes knowledge, tools, methods, processes, frameworks, approaches, and theories. The contexts of these studies are innumerable. The unit of these studies varies from individuals to organizations, using a variety of theoretical tools and methods that have fragmented the field, making it difficult to understand the map of this corpus of knowledge across this diversity.In this paper, we propose a model-based approach that on the one hand, does not delve into the details of the design object itself, but on the other hand, unifies the description of design problem at another abstraction level. The use of this abstract framework allows for describing and comparing underlying models of published design studies using the same language to place them in the right context in which design takes place and to enable to inter-relate them, to understand the wholes and the parts of design studies.Patterns of successful studies could be generated and used by researchers to improve the design of new studies, understand the outcome of existing studies, and plan follow-up studies.

scholarly journals Scalar parabolic PDEs and braids

2008 ◽  
Vol 361 (05) ◽  
pp. 2755-2788 ◽  
Author(s):  
R. W. Ghrist ◽  
R. C. Vandervorst
Keyword(s):  
Parabolic Pdes
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