scholarly journals The Dynamics of a One-Dimensional Parabolic Problem versus the Dynamics of Its Discretization

2000 ◽  
Vol 168 (1) ◽  
pp. 67-92 ◽  
Author(s):  
Simone M. Bruschi ◽  
Alexandre N. Carvalho ◽  
José G. Ruas-Filho
Keyword(s):  
Parabolic Problem ◽  
One Dimensional ◽  
Problem Versus

An elliptic-parabolic free boundary problem: continuity of the interface

1987 ◽  
Vol 106 (3-4) ◽  
pp. 327-339 ◽  
Author(s):  
J. Hulshof
Keyword(s):  
Porous Media ◽  
Weak Solution ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Fluid Flows ◽  
One Dimensional ◽  
The Maximum Principle ◽  
Partially Saturated ◽  
Physical Background ◽  
Essential Assumption

SynopsisIn this paper we establish continuity of the interface of the weak solution to an elliptic-parabolic problem. The physical background is the theory of partially saturated fluid flows in porous media. Our method is based on the maximum principle for parabolic equations. An essential assumption is that the flow is one-dimensional.

scholarly journals On The Dense Controllability for The Parabolic Problem with Time-Distributed Functional

2018 ◽  
Vol 71 (1) ◽  
pp. 9-25
Author(s):  
Irina V. Astashova ◽  
Alexey V. Filinovskiy
Keyword(s):  
Heat Equation ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Control Function ◽  
One Dimensional ◽  
Cost Functional ◽  
Control Functions ◽  
Quadratic Cost

Abstract We consider a control problem for one-dimensional heat equation with quadratic cost functional. We prove the existence and uniqueness of a control function from a prescribed set, and study the structure of the set of accessible temperature functions. We also prove the dense controllability of the problem for some set of control functions.

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