scholarly journals On the Heat Equation with a Time-Dependent Singular Potential

2002 ◽  
Vol 194 (1) ◽  
pp. 17-52
Author(s):  
Archil Gulisashvili
Keyword(s):  
Heat Equation ◽  
Singular Potential ◽  
Time Dependent

scholarly journals hp-FEM for the fractional heat equation

2020 ◽  
Author(s):  
Jens Markus Melenk ◽  
Alexander Rieder
Keyword(s):  
Finite Elements ◽  
Heat Equation ◽  
Exponential Convergence ◽  
Time Dependent ◽  
Nonlocal Operator ◽  
Time Stepping ◽  
Fractional Heat Equation ◽  
Time Dependent Problem ◽  
Hp Finite Elements ◽  
Abstract Framework

Abstract We consider a time-dependent problem generated by a nonlocal operator in space. Applying for the spatial discretization a scheme based on $hp$-finite elements and a Caffarelli–Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using $hp$-discontinuous Galerkin based time stepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the spatial domain $\varOmega $.

scholarly journals On the parabolic potentials in degenerate-type heat equation

1991 ◽  
Vol 4 (2) ◽  
pp. 147-160 ◽  
Author(s):  
Igor Malyshev
Keyword(s):  
Heat Equation ◽  
Mixed Type ◽  
Time Dependent ◽  
Degenerate Type ◽  
Theory Technique

Using distributions theory technique we introduce parabolic potentials for the heat equation with one time-dependent coefficient (not everywhere positive and continuous) at the highest space-derivative, discuss their properties, and apply obtained results to three illustrative problems. Presented technique allows to deal with some equation of the degenerate/mixed type.

Stability of optimal control of heat equation with singular potential

2014 ◽  
Vol 74 ◽  
pp. 18-23 ◽  
Author(s):  
Guojie Zheng ◽  
Bao-Zhu Guo ◽  
M. Montaz Ali
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Singular Potential

scholarly journals Time-dependent singularities in the heat equation

2015 ◽  
Vol 14 (3) ◽  
pp. 969-979 ◽  
Author(s):  
Jin Takahashi ◽  
Eiji Yanagida
Keyword(s):  
Heat Equation ◽  
Time Dependent
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