scholarly journals Degenerate nonlocal Cahn-Hilliard equations: Well-posedness, regularity and local asymptotics

2020 ◽  
Vol 37 (3) ◽  
pp. 627-651 ◽  
Author(s):  
Elisa Davoli ◽  
Helene Ranetbauer ◽  
Luca Scarpa ◽  
Lara Trussardi
Keyword(s):  
Well Posedness ◽  
Local Asymptotics

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

Local Asymptotics of Unfoldings of Edge and Corner Catastrophes

2020 ◽  
Vol 27 (4) ◽  
pp. 446-455
Author(s):  
J. I. Bova ◽  
A. S. Kryukovskii ◽  
D. S. Lukin
Keyword(s):  
Local Asymptotics

scholarly journals The BV solution of the parabolic equation with degeneracy on the boundary

2016 ◽  
Vol 14 (1) ◽  
pp. 272-282
Author(s):  
Huashui Zhan ◽  
Shuping Chen
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Well Posedness ◽  
Test Functions ◽  
The Stability

AbstractConsider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

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