On the sufficient condition for regularity of a boundary point for singular parabolic equations with non-standard growth

2011 ◽  
Vol 284 (16) ◽  
pp. 2101-2122 ◽  
Author(s):  
Igor I. Skrypnik
Keyword(s):  
Parabolic Equations ◽  
Boundary Point ◽  
Sufficient Condition ◽  
Singular Parabolic Equations

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

On the Necessity of theWiener Condition for Singular Parabolic Equations with Non-standard Growth

2011 ◽  
Vol 11 (3) ◽  
Author(s):  
Igor I. Skrypnik
Keyword(s):  
Parabolic Equations ◽  
Boundary Point ◽  
Nonlinear Parabolic Equations ◽  
Cylindrical Domain ◽  
Nonsmooth Boundary ◽  
Nonlinear Parabolic ◽  
Continuity Of Solutions ◽  
Singular Parabolic Equations

AbstractWe investigate the continuity of solutions for general nonlinear parabolic equations with non-standard growth near a nonsmooth boundary of a cylindrical domain. We prove the Wiener Criterion for the regularity of a boundary point.

scholarly journals An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Khalid Atifi ◽  
Idriss Boutaayamou ◽  
Hamed Ould Sidi ◽  
Jawad Salhi
Keyword(s):  
Numerical Solution ◽  
Parabolic Equations ◽  
Measurement Data ◽  
Gradient Methods ◽  
Stability Estimate ◽  
Inverse Source Problem ◽  
Output Least Squares ◽  
Singular Parabolic Equations ◽  
Interior Degeneracy ◽  
Least Squares Approach

The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem.

Nonlinear Singular Parabolic Equations

2020 ◽  
pp. 21-36
Author(s):  
Piotr Biler ◽  
Tadeusz Nadzieja ◽  
Andrzej Raczyński
Keyword(s):  
Parabolic Equations ◽  
Singular Parabolic Equations

scholarly journals ON A PROPERTY OF SOLUTION OF A NONLOCAL PROBLEM IN TIME FOR SINGULAR PARABOLIC EQUATIONS

2018 ◽  
Vol 6 (1-2) ◽  
Author(s):  
G. Verezhak ◽  
V. Horodetskyi
Keyword(s):  
Parabolic Equations ◽  
Nonlocal Problem ◽  
Singular Parabolic Equations

scholarly journals Carleman estimates and null controllability of a class of singular parabolic equations

2018 ◽  
Vol 8 (1) ◽  
pp. 1057-1082
Author(s):  
Runmei Du ◽  
Jürgen Eichhorn ◽  
Qiang Liu ◽  
Chunpeng Wang
Keyword(s):  
Control Systems ◽  
Parabolic Equations ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Energy Estimates ◽  
Semilinear Parabolic Equations ◽  
Linearized Equations ◽  
Singular Parabolic Equations ◽  
Semilinear Parabolic

Abstract In this paper, we consider control systems governed by a class of semilinear parabolic equations, which are singular at the boundary and possess singular convection and reaction terms. The systems are shown to be null controllable by establishing Carleman estimates, observability inequalities and energy estimates for solutions to linearized equations.

Degenerate and Singular Parabolic Equations

2011 ◽  
pp. 23-55
Author(s):  
Emmanuele DiBenedetto ◽  
Ugo Gianazza ◽  
Vincenzo Vespri
Keyword(s):  
Parabolic Equations ◽  
Singular Parabolic Equations
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