Mixed problem for nonlinear parabolic equations with variable delay

Bokalo Mykola Mykhailovych; Ilnytska Olga Volodymyrivna

Bokalo Mykola Mykhailovych ¹ , Ilnytska Olga Volodymyrivna ²

¹ Department of Mathematical Statistics and Differential Equations, Ivan Franko National University of Lviv, Lviv, 79007, Ukraine

² (Department of Differential Equations, Ivan Franko National University of Lviv, Lviv, 79007, Ukraine

Keywords: mixed problem, Dirichlet condition, nonlinear parabolic equations with variable delay, conditions of existence and uniqueness of the solution

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Abstract

A mixed initial-boundary value problem with the Dirichlet condition for a nonlinear parabolic equation with variable delay is investigated. We find conditions of the existence and uniqueness for a solution of the problem, its a’priori estimate and prove comparison theorems for solutions of the considered equations.

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ACS Style: Bokalo, M.M.; Ilnytska, O.V. Mixed problem for nonlinear parabolic equations with variable delay. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Bokalo MM, Ilnytska OV. Mixed problem for nonlinear parabolic equations with variable delay. Bukovinian Mathematical Journal. 2016; 3(1).
Chicago/Turabian Style: Mykola Mykhailovych Bokalo, Olga Volodymyrivna Ilnytska. 2016. "Mixed problem for nonlinear parabolic equations with variable delay". Bukovinian Mathematical Journal. 3 no. 1.

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