Functional Differential Parabolic Equations: Integral Transformations and Qualitative Properties of Solutions of the Cauchy Problem

Muravnik, A. B.

doi:10.1007/s10958-016-2904-0

Cited by 36 publications

(14 citation statements)

References 45 publications

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“…The following results are obtained in [34,35,[37][38][39][40][41][42]44] (see also [45], Chaps. 1-2).…”

Section: Regular Parabolic Differential-difference Equationsmentioning

confidence: 95%

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Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Muravnik

2019

Math. Model. Nat. Phenom.

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This paper presents a review of results on nonlocal problems, functional-differential equations, and their applications, obtained during several last years. The following research areas are covered: the Kato square root problem for functional-differential operators, Vlasov equations and their applications to the modelling of high-temperature plasma, specific properties of differential-difference equations with incommensurable translations, degenerate functional-differential equations and their applications, functional-differential equations with contractions and extensions of independent variables, and operational methods for parabolic and elliptic functional-differential equations.

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“…The following results are obtained in [34,35,[37][38][39][40][41][42]44] (see also [45], Chaps. 1-2).…”

Section: Regular Parabolic Differential-difference Equationsmentioning

confidence: 95%

“…The main result about the long-time behavior is as follows. The results presented in this section are obtained in [36,43] (see also [45], Chaps. 3-4).…”

Section: Singular Parabolic Functional-differential Equationsmentioning

confidence: 99%

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Muravnik

2019

Math. Model. Nat. Phenom.

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“…This potential is the negative real power of the hyperbolic operator (1). In our research we rely on methods developed in papers [34]- [41]. Namely, we use the methods of such transmutation operators as a generalized translation and the Poisson operator (see [34]- [38]), weighted spaces (see [39]- [41]) and methods of classical Riesz potentials (see [28]- [47]).…”

Section: Brief Historymentioning

confidence: 99%

Inversion of the Mixed Riesz Hyperbolic B-Potentials

Shishkina¹

2017

Int. J. of Appl. Math.

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“…In unbounded domains, problems for elliptic equations with translation operators were studied in the works of A. Muravnik [8][9][10][11]. Problems for parabolic equations with translation operators with respect to time or space variables are studied in [12].…”

Section: Introductionmentioning

confidence: 99%

Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms

Vasilyev

Зайцева

2023

Mathematics

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In this paper, we study the question of constructing explicit solutions in a half-space of a hyperbolic equation containing translation operators in space variables in all coordinate directions. Such equations are a natural generalization of classical equations of hyperbolic type, and the resulting solution relates the value of the desired function at different points of the half-space where the process takes place. To construct solutions, a classical operating scheme is used, namely, the formal application of an integral transformation. A theorem is proved that the constructed solutions are classical if the real part of the symbol of the differential-difference operator in the equation is positive. Classes of equations for which this condition is satisfied are given.

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Functional Differential Parabolic Equations: Integral Transformations and Qualitative Properties of Solutions of the Cauchy Problem

Cited by 36 publications

References 45 publications

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

Inversion of the Mixed Riesz Hyperbolic B-Potentials

Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms

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