Russian Mathematical Surveys, Volume 42, Number 5, October 1987, 1987

CONTENTS Introduction § 1. Survey of results on the asymptotic behaviour of solutions of first order non-linear equations § 2. Representation and asymptotic behaviour of the solution of the Cauchy problem for a quasilinear conservation law in the case of a monotonic initial function § 3. The stabilization to a constant of the solution of the Cauchy problem for a quasilinear conservation law References

https://doi.org/10.1070/RM1987v042n05ABEH001468

49

Markov processes and partial differential equations on a group: the space-homogeneous case

A D Bendikov

Open abstract View article, Markov processes and partial differential equations on a group: the space-homogeneous case PDF, Markov processes and partial differential equations on a group: the space-homogeneous case

CONTENTS Introduction Terminology and notation Chapter I. Potential theory of conjugate processes § 1.1. Markov processes and harmonic spaces § 1.2. Processes of class and Brelot spaces § 1.3. Processes of class and Bauer spaces Chapter II. Space-homogeneous processes on a group § 2.1. Space-homogeneous processes and harmonic structures § 2.2. Quasidiagonal processes § 2.3. An example of a non-quasidiagonal process Chapter III. Elliptic equations on a group § 3.1. Admissible distributions and multipliers § 3.2. Weak solutions of elliptic equations (-theory) § 3.3. Weyl's lemma and the hypoelliptic property References

https://doi.org/10.1070/RM1987v042n05ABEH001485

95

Homogeneous and non-homogeneous duality

V V Pashenkov

Open abstract View article, Homogeneous and non-homogeneous duality PDF, Homogeneous and non-homogeneous duality

CONTENTS Introduction § 0. Notation and terminology § 1. Strategy for constructing a homogeneous extension of Gel'fand duality § 2. Extended Stone duality § 3. Boolean models § 4. Zero-dimensional homogeneous duality and its applications References

https://doi.org/10.1070/RM1987v042n05ABEH001486

123

On the equivalence of convergence of a regularizing algorithm to the existence of a solution to an ill-posed problem

E N Domanskii

Open abstract View article, On the equivalence of convergence of a regularizing algorithm to the existence of a solution to an ill-posed problem PDF, On the equivalence of convergence of a regularizing algorithm to the existence of a solution to an ill-posed problem

CONTENTS § 1. Maslov's theorem and B-soluble families of operators § 2. The concept of a soluble operator basis § 3. Soluble operator bases and Tikhonov regularizability of the equation § 4. Soluble linear operator bases and linear finite-dimensional regularizability of the equation § 5. On a generalization of Picard's theorem References

https://doi.org/10.1070/RM1987v042n05ABEH001469

145

Aleksei Fedorovich Leont'ev (obituary)

Yu N Frolov, A A Gonchar, V V Napalkov, Sergei M Nikol'skii, A M Sedletskii, P L Ul'yanov, A G Vitushkin and Vasilii S Vladimirov

View article, Aleksei Fedorovich Leont'ev (obituary) PDF, Aleksei Fedorovich Leont'ev (obituary)

https://doi.org/10.1070/RM1987v042n05ABEH001470

153

Evgenii Mikhailovich Nikishin (obituary)

Lyudvig D Faddeev, A A Gonchar, B S Kashin, A I Kostrikin, Sergei M Nikol'skii, S P Novikov, P L Ul'yanov and A G Vitushkin

View article, Evgenii Mikhailovich Nikishin (obituary) PDF, Evgenii Mikhailovich Nikishin (obituary)

https://doi.org/10.1070/RM1987v042n05ABEH001471

161

Nikolai Grigor'evich Chudakov (obituary)

B M Berdikhin, A A Karatsuba, A F Lavrik, A V Malyshev, A G Postnikov, V G Sprindzhuk and V E Voskresenskii

View article, Nikolai Grigor'evich Chudakov (obituary) PDF, Nikolai Grigor'evich Chudakov (obituary)

https://doi.org/10.1070/RM1987v042n05ABEH001472

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Volume 42

COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY

MATHEMATICAL EVENTS IN THE USSR

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