Asymptotics for a nonlinear integral equation with a generalized heat kernel

被引：30

作者：

Ishige, Kazuhiro ^{[1
]}

Kawakami, Tatsuki ^{[2
]}

Kobayashi, Kanako ^{[1
]}

机构：

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

[2] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka 5998531, Japan

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2014年 / 14卷 / 4-5期

基金：

日本学术振兴会;

关键词：

SEMILINEAR PARABOLIC EQUATIONS; LARGE TIME BEHAVIOR; GLOBAL-SOLUTIONS; INITIAL DATA; WHOLE SPACE; DIFFUSION-EQUATIONS; SUPERCRITICAL RANGE; SLOW DECAY; R-N; EXISTENCE;

D O I：

10.1007/s00028-014-0237-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with a nonlinear integral equation (P) u(x, t) = integral (N)(R) G(x - y, t) phi(y)dy + integral(t)(0) integral(N)(R) G(x - y, t - s)f(y, s : u)dyds, Where N >= 1, phi is an element of L-infinity (R-N) boolean AND L-1(R-N, (1+vertical bar x vertical bar(K))dx for some K >= 0. Hence, G = G(x, t) is phi a generalization of the heat kernel. We are interested in the asymptotic expansions of the solution of (P) behaving like a multiple of the integral kernel G as t -> infinity.

引用

页码：749 / 777

页数：29

共 35 条

[1]

[Anonymous], 1997, Acta Mathematica Universitatis Comenianae

[2] Fractal Burgers equations [J].

Biler, P ;

Funaki, T ;

Woyczynski, WA .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 148 (01) :9-46

[3] Global and exploding solutions for nonlocal quadratic evolution problems [J].

Biler, P ;

Woyczynski, WA .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1998, 59 (03) :845-869

[4] Existence and nonexistence of global solutions of higher-order parabolic problems with slow decay initial data [J].

Caristi, G ;

Mitidieri, E .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 279 (02) :710-722

[5]

Carpio A., 1996, ANN SCUOLA NORM SU S, V23, P551

[6]

Cui S, 2001, NONLINEAR ANAL-THEOR, V43, P293

[7]

DOLBEAULT J., 2006, BANACH CTR PUBL, V74, P113

[8] Large time behavior for convection-diffusion equations in RN with asymptotically constant diffusion [J].

Duro, G ;

Zuazua, E .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (7-8) :1283-1340

[9]

Egorov YV, 2004, ADV DIFFERENTIAL EQU, V9, P1009

[10] On the necessary conditions of global existence to a quasilinear inequality in the half-space [J].

Egorov, YV ;

Galakitionov, VA ;

Kondratiev, VA ;

Pohozaev, SI .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (02) :93-98

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