Linear Second-Order Equations with Two Independent Variables

2000 ◽  
pp. 245-309
Author(s):  
J. Kevorkian
Keyword(s):  
Second Order ◽  
Independent Variables ◽  
Second Order Equations ◽  
Two Independent Variables

scholarly journals On the Cauchy problem for Dt2 − Dx(b(t)a(x))Dx

2020 ◽  
Vol 17 (01) ◽  
pp. 75-122
Author(s):  
Ferruccio Colombini ◽  
Tatsuo Nishitani
Keyword(s):  
Cauchy Problem ◽  
Differential Operators ◽  
Second Order ◽  
Gevrey Class ◽  
Independent Variables ◽  
The Cauchy Problem ◽  
Well Posed ◽  
Two Independent Variables

We consider the Cauchy problem for second-order differential operators with two independent variables [Formula: see text]. Assuming that [Formula: see text] is a nonnegative [Formula: see text] function and [Formula: see text] is a nonnegative Gevrey function of order [Formula: see text], we prove that the Cauchy problem for [Formula: see text] is well-posed in the Gevrey class of any order [Formula: see text] with [Formula: see text].

Comparative Study on Treatment Bioscouring Optimization with and without Ultrasound for 50 % of Cotton + 50 % of Flax Materials

2018 ◽  
Vol 27 ◽  
pp. 111-117
Author(s):  
Monica Pustianu ◽  
Mihaela Dochia ◽  
Simona Gavrilaş ◽  
Daniel Tomescu
Keyword(s):  
Weight Loss ◽  
Comparative Study ◽  
Treatment Time ◽  
Enzyme Concentration ◽  
Second Order ◽  
Independent Variables ◽  
Ultrasound Energy ◽  
Presence And Absence ◽  
Two Independent Variables

The research presents a comparative study regarding the optimization of two bioscouring treatments applied on 50 % of flax+50 % of cotton blended material in presence and absence of the ultrasound energy The treatments optimization was made by using a central, rotatable second order compound program with two independent variables: enzyme concentration and treatment time. The data obtained after determination of the weight loss of the treated samples fabrics were used afterwards for the bioscouring treatments optimization.

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