scholarly journals Asymptotic profile of solutions to the heat equation on thin plate with boundary heating

2021 ◽  
Vol 408 ◽  
pp. 126356
Author(s):  
Eun-Ho Lee ◽  
Woocheol Choi
Keyword(s):  
Heat Equation ◽  
Thin Plate ◽  
Asymptotic Profile

Heat equation model for rod and thin plate by partial q-difference operator

2018 ◽  
Vol 27 (1) ◽  
pp. 161-172
Author(s):  
G. Britto Antony Xavier ◽  
S. John Borg ◽  
B. Govindan ◽  
M. Meganathan
Keyword(s):  
Heat Equation ◽  
Thin Plate ◽  
Difference Operator ◽  
Equation Model

scholarly journals New Solutions of the Heat Equation and Application to Thin Plate Heat Conduction

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Heat Equation ◽  
Ordinary Differential Equations ◽  
Symmetry Group ◽  
Thin Plate ◽  
Lie Symmetry ◽  
Second Order ◽  
Group Generator ◽  
Plate Heat

Using a Lie symmetry group generator and a generalised form of Euler’s formula for solving second order ordinary differential equations, we determine new symmetries for the heat equation, leading to new solutions. As an application, we test a formula resulting from this approach on thin plate heat conduction

scholarly journals On diffusion phenomena for the linear wave equation with space-dependent damping

2014 ◽  
Vol 11 (04) ◽  
pp. 795-819 ◽  
Author(s):  
Yuta Wakasugi
Keyword(s):  
Wave Equation ◽  
Heat Equation ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Diffusion Phenomenon ◽  
Asymptotic Profile ◽  
Diffusion Phenomena

We study the diffusion phenomenon associated with the linear wave equation with space-dependent damping, and give a proof that the asymptotic profile of solutions is represented by solutions to the associated heat equation, in the L2sense.

SPECTRAL PROBLEMS ARISING IN THE STABILIZATION PROBLEM FOR THE LOADED HEAT EQUATION: A TWO-DIMENSIONAL AND MULTI-POINT CASES

2019 ◽  
Vol 7 (1) ◽  
pp. 23-37
Author(s):  
Jenaliyev M.T. ◽  
◽  
Imanberdiyev K.B. ◽  
Kassymbekova A.S. ◽  
Sharipov K.S. ◽  
...  
Keyword(s):  
Heat Equation ◽  
Two Dimensional ◽  
Stabilization Problem ◽  
Spectral Problems

Forming of thin plate with diode laser

2001 ◽  
Author(s):  
Toshiyuki Miyazaki ◽  
Masatoshi Saito ◽  
Shunro Yoshioka ◽  
Tsuyoshi Tokunaga ◽  
Tadashi Misu ◽  
...  
Keyword(s):  
Diode Laser ◽  
Thin Plate

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

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