scholarly journals Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials

2020 ◽  
Vol 26 ◽  
pp. 50
Author(s):  
Pablo Àlvarez-Caudevilla ◽  
Matthieu Bonnivard ◽  
Antoine Lemenant
Keyword(s):  
Parabolic Equations ◽  
Parabolic Problem ◽  
Decay Estimate ◽  
Convergence Result ◽  
Asymptotic Limit ◽  
Cylindrical Domain ◽  
Noncylindrical Domain ◽  
Linear Parabolic Equations ◽  
Exponential Decay Estimate ◽  
Spatio Temporal

In this paper, we observe how the heat equation in a noncylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as a parabolic version of a previous work by the first and last authors, concerning the stationary case [Alvarez-Caudevilla and Lemenant, Adv. Differ. Equ. 15 (2010) 649-688]. We provide a strong convergence result for the solution by use of energetic methods and Γ-convergence technics. Then, we establish an exponential decay estimate coming from an adaptation of an argument due to B. Simon.

scholarly journals Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

2005 ◽  
Vol 2005 (4) ◽  
pp. 523-536
Author(s):  
Yubin Yan
Keyword(s):  
Difference Method ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Approximation Scheme ◽  
Time Derivative ◽  
Nonsmooth Data ◽  
Smoothing Property ◽  
Linear Parabolic Equations ◽  
Linear Parabolic Problem ◽  
Data Error

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.

scholarly journals Asymptotics of the Solution of Bisingular Problem for a System of Linear Parabolic Equations. I

2015 ◽  
Vol 20 (1) ◽  
pp. 5-17
Author(s):  
M. V. Butuzova
Keyword(s):  
Small Parameter ◽  
Asymptotic Expansions ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Linear Parabolic Equations

Given a bisingular parabolic problem for a system of linear parabolic equations, we construct an asymptotics for the solution of any order with respect to a small parameter, without using the joining procedure for asymptotic expansions.

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

Second order linear parabolic equations in uniform spaces in $${\varvec{\mathbb {R}^{N}}}$$ R N

2016 ◽  
Vol 30 (1) ◽  
pp. 63-78
Author(s):  
Carlos Quesada ◽  
Aníbal Rodríguez-Bernal
Keyword(s):  
Parabolic Equations ◽  
Second Order ◽  
Uniform Spaces ◽  
Order Linear ◽  
Linear Parabolic Equations

Identifications of parameters in ill-posed linear parabolic equations

2004 ◽  
Vol 57 (5-6) ◽  
pp. 677-686 ◽  
Author(s):  
Chaohua Jia ◽  
Gengsheng Wang
Keyword(s):  
Parabolic Equations ◽  
Linear Parabolic Equations ◽  
Ill Posed

Long-range numerical solution of mildly non-linear parabolic equations

1971 ◽  
Vol 16 (4) ◽  
pp. 304-321 ◽  
Author(s):  
Alfred Carasso
Keyword(s):  
Numerical Solution ◽  
Long Range ◽  
Parabolic Equations ◽  
Linear Parabolic Equations ◽  
Non Linear
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