scholarly journals Lateral boundary differentiability of solutions of parabolic equations on cylindrical convex domains

2013 ◽  
Vol 404 (1) ◽  
pp. 36-46
Author(s):  
Yongpan Huang ◽  
Dongsheng Li ◽  
Lihe Wang
Keyword(s):  
Parabolic Equations ◽  
Lateral Boundary ◽  
Convex Domains ◽  
Differentiability Of Solutions

scholarly journals Continuous dependence and uniqueness for lateral Cauchy problems for linear integro-differential parabolic equations

2017 ◽  
Vol 25 (5) ◽  
pp. 617-631
Author(s):  
Alfredo Lorenzi ◽  
Luca Lorenzi ◽  
Masahiro Yamamoto
Keyword(s):  
Open Subset ◽  
Time Domain ◽  
Parabolic Equations ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Carleman Estimates ◽  
Lateral Boundary ◽  
Cauchy Problems ◽  
Additional Information ◽  
Continuous Dependence Results

AbstractVia Carleman estimates we prove uniqueness and continuous dependence results for lateral Cauchy problems for linear integro-differential parabolic equations without initial conditions. The additional information supplied prescribes the conormal derivative of the temperature on a relatively open subset of the lateral boundary of the space-time domain.

Asymptotic convergence to dipole solutions in nonlinear parabolic equations

1995 ◽  
Vol 125 (5) ◽  
pp. 877-900 ◽  
Author(s):  
Victor A. Galaktionov ◽  
Sergey A. Posashkov ◽  
Juan Luis Vazquez
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Asymptotic Behaviour ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Asymptotic Convergence ◽  
Lateral Boundary ◽  
Compactly Supported Function ◽  
Nonlinear Parabolic ◽  
General Power

We study the asymptotic behaviour as t → ∞ of the solution u = u(x, t) ≧ 0 to the quasilinear heat equation with absorption ut = (um)xx − f(u) posed for t > 0 in a half-line I = { 0 < x < ∞}. For definiteness, we take f(u) = up but the results generalise easily to more general power-like absorption terms f(u). The exponents satisfy m > 1 and p >m. We impose u = 0 on the lateral boundary {x = 0, t > 0}, and consider a non-negative, integrable and compactly supported function uo(x) as initial data. This problem is equivalent to solving the corresponding equation in the whole line with antisymmetric initial data, uo(−x) = −uo(x).

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