Interior regularity of solutions of differential equations

1964 ◽  
pp. 96-114
Author(s):  
Lars Hörmander
Keyword(s):  
Differential Equations ◽  
Regularity Of Solutions ◽  
Interior Regularity

scholarly journals Nonautonomous partial functional differential equations; existence and regularity

2017 ◽  
Vol 4 (1) ◽  
pp. 108-127 ◽  
Author(s):  
Moussa El-Khalil Kpoumiè ◽  
Khalil Ezzinbi ◽  
David Békollè
Keyword(s):  
Differential Equations ◽  
Linear Part ◽  
Functional Differential Equations ◽  
Local Existence ◽  
Sufficient Conditions ◽  
Reaction Diffusion Equation ◽  
Regularity Of Solutions ◽  
Partial Functional Differential Equations ◽  
Strict Solutions ◽  
Functional Differential

Abstract The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring the existence of the strict solutions. Finally, we consider a reaction diffusion equation with delay to illustrate the obtained results.

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