scholarly journals Controllability of degenerate and singular parabolic problems: the double strong case with Neumann boundary conditions

2019 ◽  
Vol 39 (2) ◽  
pp. 207-225 ◽  
Author(s):  
Genni Fragnelli ◽  
Dimitri Mugnai
Keyword(s):  
Boundary Conditions ◽  
Parabolic Problem ◽  
Singular Potential ◽  
Neumann Boundary ◽  
Null Controllability ◽  
Neumann Boundary Conditions ◽  
Parabolic Problems ◽  
Smooth Coefficients ◽  
Strongly Degenerate ◽  
Controllability Result

We prove a null controllability result for a parabolic problem with Neumann boundary conditions. We consider non smooth coefficients in presence of a strongly singular potential and a strongly degenerate coefficient, both vanishing at an interior point. This paper concludes the study of the Neumann case.

Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Idriss Boutaayamou ◽  
Genni Fragnelli ◽  
Lahcen Maniar
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Neumann Boundary ◽  
Spatial Domain ◽  
Neumann Boundary Conditions ◽  
Well Posedness ◽  
Degeneracy Point ◽  
Inverse Source Problems ◽  
Interior Degeneracy

AbstractWe consider a parabolic problem with degeneracy in the interior of the spatial domain and we focus on the well-posedness of the problem and on inverse source problems. The novelties of the present paper are two. First, the degeneracy point is in the interior of the spatial domain. Second, we consider Neumann boundary conditions so that no previous result can be adapted to this situation.

scholarly journals LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS

2011 ◽  
Vol 53 (3) ◽  
pp. 569-575 ◽  
Author(s):  
CRISTIAN ENACHE
Keyword(s):  
Boundary Conditions ◽  
Lower Bounds ◽  
Blow Up ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Neumann Boundary Conditions ◽  
Parabolic Problems ◽  
Non Linear ◽  
Inequality Technique ◽  
Initial Boundary Value

AbstractThis paper deals with some non-linear initial-boundary value problems under homogeneous Neumann boundary conditions, in which the solutions may blow up in finite time. Using a first-order differential inequality technique, lower bounds for blow-up time are determined.

Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions

2012 ◽  
Vol 142 (3) ◽  
pp. 625-631 ◽  
Author(s):  
L. E. Payne ◽  
G. A. Philippin
Keyword(s):  
Boundary Conditions ◽  
Global Solution ◽  
Lower Bounds ◽  
Blow Up ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Time Dependent ◽  
Parabolic Problems

This paper deals with the blow-up of solutions to a class of parabolic problems with time-dependent coefficients under homogeneous Neumann boundary conditions. For one set of problems in this class we show that no global solution can exist. For another we derive lower bounds for the time of blow-up when blow-up occurs.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

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