On the Closeness of Solutions of Unperturbed and Hyperbolized Heat Equations with Discontinuous Initial Data

2018 ◽  
Vol 98 (1) ◽  
pp. 391-395 ◽  
Author(s):  
T. E. Moiseev ◽  
E. E. Myshetskaya ◽  
V. F. Tishkin
Keyword(s):  
Initial Data ◽  
Heat Equations ◽  
Discontinuous Initial Data

scholarly journals On the proximity of solutions of unperturbed and hyperbolized heat equations for discontinuous initial data

2017 ◽  
pp. 1-15
Author(s):  
Tikhon Evgenievich Moiseev ◽  
Elena Evgenievna Myshetskaya ◽  
Vladimir Fedorovich Tishkin
Keyword(s):  
Initial Data ◽  
Heat Equations ◽  
Discontinuous Initial Data

scholarly journals On the Proximity of Solutions of Unperturbed and Hyperbolized Heat Equations for Discontinuous Initial Data

2018 ◽  
Vol 481 (6) ◽  
pp. 605-609
Author(s):  
E. Myshetskaya ◽  
◽  
V. Tishkin ◽  
T. Moiseev ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Heat Equations ◽  
Discontinuous Initial Data

scholarly journals Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations

2020 ◽  
Vol 10 (1) ◽  
pp. 353-370 ◽  
Author(s):  
Hans-Christoph Grunau ◽  
Nobuhito Miyake ◽  
Shinya Okabe
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Fourth Order ◽  
Parabolic Equations ◽  
Sufficient Conditions ◽  
Nonlinear Parabolic Equations ◽  
Heat Equations ◽  
Cauchy Problems ◽  
The Cauchy Problem ◽  
Positivity Of Solutions

Abstract This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth order have no positivity preserving property due to the change of sign of the fundamental solution. One has eventual local positivity for positive initial data, but on short time scales, one will in general have also regions of negativity. The first goal of this paper is to find sufficient conditions on initial data which ensure the existence of solutions to the Cauchy problem for the linear biharmonic heat equation which are positive for all times and in the whole space. The second goal is to apply these results to show existence of globally positive solutions to the Cauchy problem for a semilinear biharmonic parabolic equation.

scholarly journals Delay differential systems with discontinuous initial data and existence and uniqueness theorems for systems with impulse and delay

1994 ◽  
Vol 7 (1) ◽  
pp. 49-67 ◽  
Author(s):  
S. V. Krishna ◽  
A. V. Anokhin
Keyword(s):  
Initial Data ◽  
Existence And Uniqueness ◽  
Fixed Time ◽  
Impulsive System ◽  
Number Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Discontinuous Initial Data ◽  
Delay Differential Systems ◽  
Delay Differential

The main purpose of this paper is to discuss some qualitative aspects of differential equations with delays and impulses. Such systems are encountered in modeling the dynamics of prices and cultured populations. However, any such discussion has to be based on some existence and uniqueness results for delay equations with discontinuous initial data. This is the content of the first part of the paper. For an impulsive system, we observe a phenomenon of existence of infinite number of solutions subject to impulses arbitrarily close to a fixed time. Conditions, when such solutions exist and when they do not, are discussed.

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