On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition

The aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by...

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Main Authors:	Abdelkader Djerad, Ameur Memou, Ali Hameida
Format:	Article
Language:	English
Published:	MDPI AG 2021-08-01
Series:	Axioms
Subjects:	energy inequality integral boundary conditions strong solution weak solution second order parabolic equation
Online Access:	https://www.mdpi.com/2075-1680/10/3/181

id	doaj-98b48ab145244d02b7886cb0bf32f6c0
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spelling	doaj-98b48ab145244d02b7886cb0bf32f6c02021-09-25T23:44:49ZengMDPI AGAxioms2075-16802021-08-011018118110.3390/axioms10030181On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal ConditionAbdelkader Djerad0Ameur Memou1Ali Hameida2Laboratoire du Mathematique Pure et Appliquée, Department of Mathematics, University of Msila, Msila 28000, AlgeriaDepartment of Mathematics, University of Msila, Msila 28000, AlgeriaDepartment of Mathematics, University of Constantine 1, Constantine 25000, AlgeriaThe aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense using a functional analysis method. Then by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.https://www.mdpi.com/2075-1680/10/3/181energy inequalityintegral boundary conditionsstrong solutionweak solutionsecond order parabolic equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abdelkader Djerad Ameur Memou Ali Hameida
spellingShingle	Abdelkader Djerad Ameur Memou Ali Hameida On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition Axioms energy inequality integral boundary conditions strong solution weak solution second order parabolic equation
author_facet	Abdelkader Djerad Ameur Memou Ali Hameida
author_sort	Abdelkader Djerad
title	On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition
title_short	On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition
title_full	On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition
title_fullStr	On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition
title_full_unstemmed	On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition
title_sort	on a nonlinear mixed problem for a parabolic equation with a nonlocal condition
publisher	MDPI AG
series	Axioms
issn	2075-1680
publishDate	2021-08-01
description	The aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense using a functional analysis method. Then by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem.
topic	energy inequality integral boundary conditions strong solution weak solution second order parabolic equation
url	https://www.mdpi.com/2075-1680/10/3/181
work_keys_str_mv	AT abdelkaderdjerad onanonlinearmixedproblemforaparabolicequationwithanonlocalcondition AT ameurmemou onanonlinearmixedproblemforaparabolicequationwithanonlocalcondition AT alihameida onanonlinearmixedproblemforaparabolicequationwithanonlocalcondition
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On a Nonlinear Mixed Problem for a Parabolic Equation with a Nonlocal Condition

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