scholarly journals New Maximal Regularity Results for the Heat Equation in Exterior Domains, and Applications

2013 ◽  
pp. 101-128
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha
Keyword(s):  
Heat Equation ◽  
Maximal Regularity ◽  
Exterior Domains ◽  
Regularity Results

Bounded solutions of linear periodic abstract parabolic equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 135-159 ◽  
Author(s):  
Alessandra Lunardi
Keyword(s):  
Banach Space ◽  
Parabolic Equations ◽  
Evolution Operator ◽  
Maximal Regularity ◽  
Analytic Semigroups ◽  
Bounded Solutions ◽  
Time Intervals ◽  
Abstract Parabolic Equations ◽  
Regularity Results ◽  
General Banach Space

SynopsisWe study the asymptotic behaviour of the parabolic evolution operatorG(t,s) associated with a family of generators of analytic semigroups {A(t);t∊ ℝ} in general Banach space, under the periodicity assumptionA(t) =A(t+T). We find new maximal regularity results for the bounded solutions of abstract nonhomogeneous parabolic equations in unbounded time intervals.

scholarly journals A discrete free boundary problem

2015 ◽  
Vol Volume 20 - 2015 - Special... ◽  
Author(s):  
Imme Berg
Keyword(s):  
Free Boundary ◽  
Heat Equation ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
International Audience ◽  
Regularity Results

International audience We study the free boundary problem in a nonstandard setting of infinitesimal discretisations of the heat equation. In particular we derive regularity results of solutions and the free boundary, in terms of S-continuity and S-differentiability Nous étudions le problème de la frontière libre dans le contexte non-standard de discrétisations infinitésimales de l'équation de la chaleur. En particulier nous prouvons des résultats de régularité des solutions et de la frontière libre, en termes de S-continuité et de S-dérivabilité.

New regularity results for the heat equation in triangular domains

SeMA Journal ◽  
2022 ◽  
Author(s):  
Yassine Benia ◽  
Boubaker-Khaled Sadallah
Keyword(s):  
Heat Equation ◽  
Regularity Results

scholarly journals Some regularity results on the ‘relativistic’ heat equation

2008 ◽  
Vol 245 (12) ◽  
pp. 3639-3663 ◽  
Author(s):  
F. Andreu ◽  
V. Caselles ◽  
J.M. Mazón
Keyword(s):  
Heat Equation ◽  
Regularity Results

scholarly journals Global in Space Regularity Results for the Heat Equation with Robin-Neumann Type Boundary Conditions in Time-varying Domains

2019 ◽  
pp. 355-370
Author(s):  
Tahir Boudjeriou ◽  
Arezki Kheloufi
Keyword(s):  
Sobolev Space ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Decomposition Method ◽  
Global Regularity ◽  
Domain Decomposition Method ◽  
Time Varying ◽  
Neumann Type ◽  
Type Boundary ◽  
Regularity Results

This article deals with the heat equation @tu @2x u = f in D; D = {(t; x) 2 R2 : a < t < b; (t) < x < +1} with the function satisfying some conditions and the problem is supplemented with boundary conditions of Robin-Neumann type. We study the global regularity problem in a suitable parabolic Sobolev space. We prove in particular that for f 2 L2(D) there exists a unique solution u such that u; @tu; @jx u 2 L2 (D) ; j = 1; 2: The proof is based on the domain decomposition method. This work complements the results obtained in [10].

scholarly journals Sample paths of white noise in spaces with dominating mixed smoothness

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Felix Hummel
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Space Dimension ◽  
Regularity Of Solutions ◽  
Time Direction ◽  
Sample Paths ◽  
Regularity Results ◽  
Boundary Noise ◽  
Dominating Mixed Smoothness ◽  
Mixed Smoothness

AbstractThe sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white noise is actually much smoother than the known sharp regularity results in isotropic spaces suggest. An application of our techniques yields new results for the regularity of solutions of Poisson and heat equation on the half space with boundary noise. The main novelty is the flexible treatment of the interplay between the singularity at the boundary and the smoothness in tangential, normal and time direction.

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