On absence of global solutions of quasilinear differential-convolutional inequalities

被引：3

作者：

Muravnik, A. B. ^{[1
,2
]}

机构：

[1] JSC Concern Sozvezdie, Voronezh, Russia

[2] RUDN Univ, Peoples Friendship Univ Russia, Nikolskii Math Inst, Moscow, Russia

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2020年 / 65卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

V; Volpert; Quasilinear inequalities; convolutional terms; nonlocal terms; global solutions; nonexistence; DIRECTED POLYMER; KPZ; EXISTENCE; EQUATIONS; BURGERS;

D O I：

10.1080/17476933.2019.1639049

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

From a unique viewpoint, elliptic and parabolic second-order inequalities with quasilinear KPZ-type terms and nonlocal convolutional terms arising in the description of reaction-diffusion processes, neural networks, and nonlocal phase transitions are investigated. Sufficient conditions of the absence of their global solutions, i.e. necessary conditions of their global solvability, are found.

引用

页码：977 / 985

页数：9

共 31 条

[1]

Akhmetov DR, 2002, ELECTRON J DIFFER EQ

[2] SOME EXISTENCE THEOREMS FOR SEMI-LINEAR ELLIPTIC EQUATIONS [J].

AMANN, H ;

CRANDALL, MG .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1978, 27 (05) :779-790

[3] Spectral properties of burgers and KPZ turbulence [J].

Anh, VV ;

Leonenko, NN ;

Sakhno, LM .

JOURNAL OF STATISTICAL PHYSICS, 2006, 122 (05) :949-974

[4] Gaussian Multiplicative Chaos and KPZ Duality [J].

Barral, Julien ;

Jin, Xiong ;

Rhodes, Remi ;

Vargas, Vincent .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 323 (02) :451-485

[5] KPZ in One Dimensional Random Geometry of Multiplicative Cascades [J].

Benjamini, Itai ;

Schramm, Oded .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 289 (02) :653-662

[6] Occupation times of long-range exclusion and connections to KPZ class exponents [J].

Bernardin, Cedric ;

Goncalves, Patricia ;

Sethuraman, Sunder .

PROBABILITY THEORY AND RELATED FIELDS, 2016, 166 (1-2) :365-428

[7]

Bitsadze A.V., 1977, DIFFER EQU, V13, P1993

[8] Almost periodic traveling waves of nonlocal evolution equations [J].

Chen, FX .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 50 (06) :807-838

[9] Universality of slow decorrelation in KPZ growth [J].

Corwin, Ivan ;

Ferrari, Patrik L. ;

Peche, Sandrine .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2012, 48 (01) :134-150

[10]

Fife P.C., 2002, HDB DYNAMICAL SYSTEM, V2, P677

← 1 2 3 4 →