scholarly journals Self-similar factor approximants for evolution equations and boundary-value problems

2008 ◽  
Vol 323 (12) ◽  
pp. 3074-3090 ◽  
Author(s):  
E.P. Yukalova ◽  
V.I. Yukalov ◽  
S. Gluzman
Keyword(s):  
Boundary Value Problems ◽  
Evolution Equations ◽  
Boundary Value ◽  
Self Similar ◽  
Similar Factor

scholarly journals Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

2011 ◽  
Vol 152 (3) ◽  
pp. 473-496 ◽  
Author(s):  
DAVID A. SMITH
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Evolution Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Transform Method ◽  
Arbitrary Boundary ◽  
Initial Boundary Value ◽  
Well Posed

AbstractWe study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series.The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

scholarly journals The profile near quenching time for the solution of a singular semilinear heat equation

1997 ◽  
Vol 40 (3) ◽  
pp. 437-456 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Bei Hu
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Quenching Rate ◽  
Semilinear Heat Equation ◽  
Self Similar ◽  
Initial Boundary Value ◽  
Quenching Time

We study the profile near quenching time for the solutions of the first and second initial boundary value problems (IBVP) for a semilinear heat equation. Under certain conditions, one-point quenching occurs for both first and second IBVPs. Furthermore, we derive the asymptotic self-similar quenching rate for both problems.

Sign in / Sign up

Export Citation Format

Share Document