A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations

Marhoune, A. L.; Lakhal, Fahim

doi:10.1155/2009/975601

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…Boundary-value problems for parabolic equations with integral boundary condition are investigated by Batten (1963); Bouziani and Benouar (1998); Cannon (1963);(1984); Cannon et al (1987); Ionkin (1977); Kamynin (1964); Field and Komkov (1992); Shi (1993); Marhoune and Bouzit (2005); Marhoune and Hameida (2008); Denche et al (1994); Denche and Marhoune (2001); Marhoune and Latrous (2008); Yurchuk (1986) and many references therein. The problem with integral one space-variable (respectively two space-variables) condition is studied in Fairweather and Saylor (1991) and Denche and Marhoune (2000) (respectively in Marhoune (2007) and Marhoune and Lakhal (2009)).…”

Section: < < ≤ < ≤ ≤mentioning

confidence: 99%

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An Integral Two Space-Variables Condition for Parabolic Equations

Seetha¹

2012

Journal of Mathematics and Statistics

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Section: < < ≤ < ≤ ≤mentioning

confidence: 99%

“…If we introduce the smoothing operators with respect to t (Yurchuk, 1986;Marhoune and Lakhal, 2009 (g ) (t) g (t) g(t)…”

Section: Solvability Of the Problemmentioning

confidence: 99%

An Integral Two Space-Variables Condition for Parabolic Equations

Seetha¹

2012

Journal of Mathematics and Statistics

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Well posedness of a nonlinear mixed problem for a parabolic equation with integral condition

Djerad¹,

Memou²,

Hameida

2021

Bound Value Probl

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The aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and the density of the operator range generated by the considered problem is proved by using the functional analysis method. Subsequently, by applying an iterative process based on the obtained results for the linear problem, the existence, uniqueness of the weak solution of the nonlinear problems is established.

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

Djerad¹,

Memou²,

Hameida

2021

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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.

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A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations

Cited by 3 publications

References 10 publications

An Integral Two Space-Variables Condition for Parabolic Equations

An Integral Two Space-Variables Condition for Parabolic Equations

Well posedness of a nonlinear mixed problem for a parabolic equation with integral condition

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

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