scholarly journals Lateral boundary differentiability of solutions of parabolic equations in nondivergence form

2013 ◽  
Vol 255 (10) ◽  
pp. 3491-3504
Author(s):  
Yongpan Huang ◽  
Dongsheng Li ◽  
Lihe Wang
Keyword(s):  
Parabolic Equations ◽  
Lateral Boundary ◽  
Nondivergence Form ◽  
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).

WEIGHTED SOLVABILITY FOR PARABOLIC EQUATIONS WITH PARTIALLY BMO COEFFICIENTS AND ITS APPLICATIONS

2014 ◽  
Vol 96 (3) ◽  
pp. 396-428
Author(s):  
LIN TANG
Keyword(s):  
Bounded Domain ◽  
Parabolic Equations ◽  
Global Regularity ◽  
Morrey Spaces ◽  
Divergence Form ◽  
Bounded Mean Oscillation ◽  
Nondivergence Form ◽  
Mean Oscillation ◽  
Bmo Coefficients

AbstractWe consider the weighted $L_p$ solvability for divergence and nondivergence form parabolic equations with partially bounded mean oscillation (BMO) coefficients and certain positive potentials. As an application, global regularity in Morrey spaces for divergence form parabolic operators with partially BMO coefficients on a bounded domain is established.

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