On the Asymptotics of the Solution of the Cauchy Problem for Some Differential-Difference Parabolic Equations

Muravnik, A. B.

doi:10.1007/s10625-005-0190-6

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…However, some interesting works contain equations with modifications of the spatial variable in the unknown function that are motivated by the nonlinear optics, studied in a number of papers (see previous studies); for instance, in one study, the author studied the Cauchy problem for the difference‐differential parabolic equation

\frac{\partial u}{\partial t} = normalΔ u + \sum_{h \in M} a_{h} u (x - h, t),

where

scriptM

is a finite set of vectors in

R^{n}

parallel to coordinate axes and the coefficients a h are real. It should be noted that parabolic functional differential equation arise in the investigation of nonlinear optic systems with 2‐dimensional feedback(see previous studies and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Some inverse problems for the nonlocal heat equation with Caputo fractional derivative

Torebek

Tapdıgoglu

2017

Math Methods in App Sciences

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\frac{\partial u}{\partial t} = normalΔ u + \sum_{h \in M} a_{h} u (x - h, t),

where

scriptM

is a finite set of vectors in

R^{n}

Section: Introductionmentioning

confidence: 99%

Some inverse problems for the nonlocal heat equation with Caputo fractional derivative

Torebek

Tapdıgoglu

2017

Math Methods in App Sciences

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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: 93%

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

Muravnik

2016

J Math Sci

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On the Asymptotics of the Solution of the Cauchy Problem for Some Differential-Difference Parabolic Equations

Cited by 7 publications

References 9 publications

Some inverse problems for the nonlocal heat equation with Caputo fractional derivative

Some inverse problems for the nonlocal heat equation with Caputo fractional derivative

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

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

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