Finite Speed of Propagation and Waiting Time for Local Solutions of Degenerate Equations in Viscoelastic Media or Heat Flows with Memory

被引：0

作者：

Antontsev S.N. ^{[1
,2
,3
]}

Díaz J.I. ^{[4
]}

机构：

[1] M.A. Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk

[2] Novosibirsk State University, Novosibirsk

[3] CMAF-CIO, University of Lisbon, Lisbon

[4] Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid

来源：

Journal of Elliptic and Parabolic Equations | 2016年 / 2卷 / 1-2期

基金：

俄罗斯科学基金会;

关键词：

35K92; 45K05; finite speed of propagation; heat flows with memory; non-linear viscoelastic equation; Nonlocal equation; waiting time property;

D O I：

10.1007/BF03377402

中图分类号：

学科分类号：

摘要：

The finite speed of propagation (FSP) was established for certain materials in the 70’s by the American school (Gurtin, Dafermos, Nohel, etc.) for the special case of the presence of memory effects. A different approach can be applied by the construction of suitable super and sub-solutions (Crandall, Nohel, Díaz and Gomez, etc.). In this paper we present an alternative method to prove (FSP) which only uses some energy estimates and without any information coming from the characteristics analysis. The waiting time property is proved for the first time in the literature for this class of nonlocal equations. © 2016, Orthogonal Publishing and Springer International Publishing.

引用

页码：207 / 216

页数：9

共 50 条

[21] Solutions of Hyperbolic System of Time Fractional Partial Differential Equations for Heat Propagation
Sankeshwari, Sagar
Kulkarni, Vinayak
APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, 2024, 19 (01):
[22] Finite time extinction for solutions to fast diffusion stochastic porous media equations
Barbu, Viorel
Da Prato, Giuseppe
Roeckner, Michael
COMPTES RENDUS MATHEMATIQUE, 2009, 347 (1-2) : 81 - 84
[23] FINITE SPEED OF PROPAGATION AND ALGEBRAIC TIME DECAY OF SOLUTIONS TO A GENERALIZED THIN FILM EQUATION
Min, Lihua
Yang, Xiaoping
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (02) : 543 - 566
[24] NONLOCAL TIME-POROUS MEDIUM EQUATION: WEAK SOLUTIONS AND FINITE SPEED OF PROPAGATION
Djida, Jean-Daniel
Nieto, Juan J.
Area, Ivan
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 4031 - 4053
[25] The Long-Time Stability of Solutions for Intermittently Controlled Viscoelastic Wave Equations with Memory Terms
Liu, Zhiqing
Fang, Zhong Bo
Applied Mathematics and Optimization, 2021, 83 (03): : 1991 - 2016
[26] The Long-Time Stability of Solutions for Intermittently Controlled Viscoelastic Wave Equations with Memory Terms
Zhiqing Liu
Zhong Bo Fang
Applied Mathematics & Optimization, 2021, 83 : 1991 - 2016
[27] The Long-Time Stability of Solutions for Intermittently Controlled Viscoelastic Wave Equations with Memory Terms
Liu, Zhiqing
Fang, Zhong Bo
APPLIED MATHEMATICS AND OPTIMIZATION, 2021, 83 (03): : 1991 - 2016
[28] FINITE TIME BLOWUP AND GLOBAL SOLUTIONS OF NONLINEAR HEAT EQUATIONS IN MATRIX GEOMETRY
Li, Jiaojiao
Ma, Li
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2017, 18 (12) : 2155 - 2162
[29] Finite-difference time-domain method for modelling of seismic wave propagation in viscoelastic media
Kalyani, V. K.
Pallavika
Chakraborty, S. K.
APPLIED MATHEMATICS AND COMPUTATION, 2014, 237 : 133 - 145
[30] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO NONCLASSICAL DIFFUSION EQUATIONS WITH DEGENERATE MEMORY AND A TIME-DEPENDENT PERTURBED PARAMETER
Zhang, Jiangwei
Xie, Zhe
Xie, Yongqin
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 2024 (22) : 1 - 27

← 1 2 3 4 5 →