TIME-DEPENDENT SINGULARITIES IN THE HEAT EQUATION

被引：17

作者：

Takahashi, Jin ^{[1
]}

Yanagida, Eiji ^{[1
]}

机构：

[1] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 03期

关键词：

Heat equation; time-dependent singularity; removable singularity; asymptotic behavior; Holder continuity; SEMILINEAR PARABOLIC EQUATIONS; LINEAR ELLIPTIC-EQUATIONS; REMOVABLE SINGULARITIES;

D O I：

10.3934/cpaa.2015.14.969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider solutions of the heat equation with time-dependent singularities. It is shown that a singularity is removable if it is weaker than the order of the fundamental solution of the Laplace equation. Some examples of non-removable singularities are also given, which show the optimality of the condition for removability.

引用

页码：969 / 979

页数：11

共 50 条

[41] Riemann problem for a general variable coefficient Burgers equation with time-dependent damping
De la Cruz, Richard
Lu, Yun-guang
Wang, Xian-ting
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2024, 162
[42] Control and inverse problems for the heat equation with strong singularities
Avdonin, Sergei
Avdonina, Nina
Edward, Julian
Nurtazina, Karlygash
SYSTEMS & CONTROL LETTERS, 2021, 148
[43] A Revised Approach for One-Dimensional Time-Dependent Heat Conduction in a Slab
Caffagni, A.
Angeli, D.
Barozzi, G. S.
Polidoro, S.
JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME, 2013, 135 (03):
[44] On a multi-dimensional initial inverse heat problem with a time-dependent coefficient
Khanh, C. D.
Tuan, N. H.
APPLIED MATHEMATICS IN ENGINEERING AND RELIABILITY, 2016, : 255 - 268
[45] Asymptotically free property of the solutions of an abstract linear hyperbolic equation with time-dependent coefficients
Yamazaki, Taeko
ASYMPTOTIC ANALYSIS, 2016, 97 (1-2) : 165 - 187
[46] Bistable equation with discontinuous density dependent diffusion with degenerations and singularities
Drabek, Pavel
Zahradnikova, Michaela
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2021, (61) : 1 - 16
[47] Determination of an additive time- and space-dependent coefficient in the heat equation
Huntul, Mousa
Lesnic, Daniel
Johansson, Tomas
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 2018, 28 (06) : 1352 - 1373
[48] Restoration of the merely time-dependent lowest term in a linear Bi-flux diffusion equation
Alosaimi, M.
Tekin, I.
Cetin, M. A.
COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (08)
[49] Simultaneous reconstruction of time-dependent coefficients in the parabolic equation from over-specification conditions
Huntul, M. J.
RESULTS IN APPLIED MATHEMATICS, 2021, 12
[50] A New Carleman Inequality for a Heat Equation in Presence of Singularities and Controllability Consequences
Sadali, D.
Moulay, M. S.
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2021, 27 (01) : 51 - 65

← 1 2 3 4 5 →