Existence of a Solution to the Cauchy Problem for the Aggregation Equation in Hyperbolic Space

被引：0

作者：

Vildanova, V. F. ^{[1
]}

机构：

[1] Bashkir State Pedag Univ M Akmulla, 3a Oktyabrskoj Revoljucii Str, Ufa 450008, Russia

来源：

RUSSIAN MATHEMATICS | 2020年 / 64卷 / 07期

基金：

俄罗斯基础研究基金会;

关键词：

aggregation equation; solution existence; hyperbolic space; UNIQUENESS;

D O I：

10.3103/S1066369X2007004X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In hyperbolic space, we consider the Cauchy problem for the aggregation equation. Non-negative initial function is bounded and summable. We prove the existence of a weak solution on a small time interval. In the case where the kernel of the integral operator is smooth and rapidly decreases at infinity, the existence of a bounded solution on an arbitrary time interval is proved.

引用

页码：27 / 37

页数：11

共 9 条

[1] EXISTENCE AND UNIQUENESS OF SOLUTIONS TO AN AGGREGATION EQUATION WITH DEGENERATE DIFFUSION [J].

Bertozzi, Andrea L. ;

Slepcev, Dejan .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2010, 9 (06) :1617-1637

[2] Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems [J].

Carrillo, J ;

Wittbold, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 156 (01) :93-121

[3] ADMISSIBLE CONDITIONS FOR PARABOLIC EQUATIONS DEGENERATING AT INFINITY [J].

Kamin, Sh. ;

Pozio, M. A. ;

Tesei, A. .

ST PETERSBURG MATHEMATICAL JOURNAL, 2008, 19 (02) :239-251

[4] Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces [J].

Mukminov, F. Kh. .

SBORNIK MATHEMATICS, 2017, 208 (08) :1187-1206

[5] Well-posedness of the Cauchy problem for nonlinear parabolic equations with variable density in the hyperbolic space [J].

Punzo, Fabio .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2012, 19 (04) :485-501

[6]

Sobolev S.L., 2008, Translations of Mathematical Monographs, V90

[7] Existence and uniqueness of a weak solution of an integro-differential aggregation equation on a Riemannian manifold [J].

Vil'danova, V. F. .

SBORNIK MATHEMATICS, 2020, 211 (02) :226-257

[8] Existence and uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion of general form [J].

Vil'danova, V. F. .

SBORNIK MATHEMATICS, 2018, 209 (02) :206-221

[9]

Vildanova V.F., 2017, CMFD PEOPLES FRIENDS, V63, P557

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