Eigenvalues of the Laplacian and the Heat Equation

1981 ◽  
Vol 88 (9) ◽  
pp. 686 ◽  
Author(s):  
Jozef Dodziuk
Keyword(s):  
Heat Equation ◽  
Eigenvalues Of The Laplacian

Eigenvalues of the Laplacian and the Heat Equation

1981 ◽  
Vol 88 (9) ◽  
pp. 686-695 ◽  
Author(s):  
Jozef Dodziuk
Keyword(s):  
Heat Equation ◽  
Eigenvalues Of The Laplacian

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

ODE compensation for an unstable heat equation

2020 ◽  
Author(s):  
Xiu-Fang Yu ◽  
Jun-Min Wang
Keyword(s):  
Heat Equation

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.

Finite degrees of freedom for the refined blow-up profile of the semilinear heat equation

2017 ◽  
Vol 50 (5) ◽  
pp. 1241-1282 ◽  
Author(s):  
Van Tien Nguyen ◽  
Hatem Zaag
Keyword(s):  
Heat Equation ◽  
Degrees Of Freedom ◽  
Blow Up ◽  
Semilinear Heat Equation

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

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