A continuous dependence result for one-dimensional nonlinear dielectrics

1987 ◽  
Vol 25 (6) ◽  
pp. 755-758 ◽  
Author(s):  
R.E. Craine
Keyword(s):  
Continuous Dependence ◽  
One Dimensional ◽  
Dependence Result

ON DYNAMICAL MODEL OF DRILLING WELLS

1999 ◽  
Vol 09 (09) ◽  
pp. 1705-1718 ◽  
Author(s):  
G. CHAKVETADZE ◽  
A. STEPIN
Keyword(s):  
Continuous Dependence ◽  
Dimensionless Parameter ◽  
Invariant Probability Measure ◽  
Sufficient Condition ◽  
Weak Mixing ◽  
Absolutely Continuous ◽  
Stochastic Perturbations ◽  
One Dimensional ◽  
Absolutely Continuous Invariant ◽  
Mixing Property

A family of one-dimensional mappings and their stochastic perturbations, related to the determining of cogged bits efficiency, is studied. A sufficient condition for the existence of absolutely continuous invariant probability measure is given, and the weak mixing property of this measure is established. We formulate and discuss the results concerning the stochastic stability of the invariant measure and its continuous dependence on the dimensionless parameter of the model. Some new problems are also outlined.

WELL-POSEDNESS AND APPROXIMATION FOR A ONE-DIMENSIONAL MODEL FOR SHAPE MEMORY ALLOYS

2005 ◽  
Vol 15 (09) ◽  
pp. 1301-1327 ◽  
Author(s):  
FERDINANDO AURICCHIO ◽  
ULISSE STEFANELLI
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Space Dimension ◽  
Constitutive Law ◽  
Well Posedness ◽  
Differential Model ◽  
One Dimensional ◽  
Material Constitutive Relation ◽  
Dependence Result ◽  
Discretization Procedure

This paper addresses a one-dimensional differential model describing the super-elastic effect in shape memory alloys. After a preliminary discussion on the model, we focus our attention on the study of the material constitutive relation and prove well-posedness and approximation results for some related initial value problem. Then, we turn our attention to the coupling of the constitutive law with a quasi-static momentum relation and solve the full PDE boundary value problem in one space dimension. In particular, we provide an existence and continuous dependence result and fully develop a spacetime discretization procedure.

scholarly journals On connection between the order of a stationary one-dimensional dispersive equation and the growth of its convective term

2021 ◽  
Vol 39 (3) ◽  
pp. 157-175
Author(s):  
Nikolai Andreevitch Larkin ◽  
Jackson Luchesi
Keyword(s):  
Boundary Value Problem ◽  
Regular Solution ◽  
Continuous Dependence ◽  
Boundary Value ◽  
Critical Values ◽  
Convective Term ◽  
Dispersive Equation ◽  
One Dimensional

A boundary value problem for a stationary nonlinear dispersive equation of 2l+1 order with a convective term in the form u^ku_x, k\in N was considered on an interval (0,L). The existence, uniqueness and continuous dependence  of a regular solution as well as a relation between the order l and critical values of k of the equation have been established.

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