LOCAL WELL POSEDNESS OF CAUCHY PROBLEM FOR VISCOUS DIFFUSION EQUATIONS

被引：2

作者：

Liu, Yacheng ^{[1
]}

Xu, Runzhang ^{[2
]}

机构：

[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Peoples R China

[2] Harbin Engn Univ, Coll Automat, Harbin 150001, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2009年 / 20卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Viscous diffusion equations; Cauchy problem; W-k; W-p solution; blow up; CAHN-HILLIARD EQUATION;

D O I：

10.1142/S0129167X09005364

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the Cauchy problem of multi-dimensional viscous diffusion equations. By using an equivalent integral equations, we get the existence of local W-k,W-p solutions. And we prove the finite time blow up of solutions under appropriate conditions.

引用

页码：509 / 519

页数：11

共 50 条

[21] Well-Posedness Of A Cauchy Problem Involving Nonlinear Fractal Dissipative Equations
Luo, Yuwen
APPLIED MATHEMATICS E-NOTES, 2010, 10 : 112 - 118
[22] On the well-posedness of the Cauchy problem for some nonlocal nonlinear Schrodinger equations
Albert, John
Kahlil, Estapraq
NONLINEARITY, 2017, 30 (06) : 2308 - 2333
[23] Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones
Yakovleva, T. I.
SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (02) : 363 - 372
[24] Well-posedness of the cauchy problem for an inclusion
I. V. Mel’nikova
Differential Equations, 2004, 40 : 1512 - 1516
[25] Well-posedness of the cauchy problem for an inclusion
I. V. Mel’nikova
Differential Equations, 2004, 40 : 1512 - 1516
[26] Well-posedness of the Cauchy problem for an inclusion
Mel'nikova, IV
DIFFERENTIAL EQUATIONS, 2004, 40 (10) : 1512 - 1516
[27] Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics
Oishi, Kenta
Shibata, Yoshihiro
MATHEMATICS, 2021, 9 (05) : 1 - 33
[28] ON A NECESSARY CONDITION FOR THE WELL-POSEDNESS OF THE CAUCHY-PROBLEM FOR EVOLUTION-EQUATIONS
SADAMATSU, T
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1989, 29 (02): : 221 - 231
[29] Well-posedness of the Cauchy problem for the coupled system of the Schrodinger-KdV equations
Guo, BL
Miao, CX
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 1999, 15 (02): : 215 - 224
[30] Criteria for the well-posedness of the cauchy problem for differential operator equations of arbitrary order
Vlasenko L.A.
Piven' A.L.
Rutkas A.G.
Ukrainian Mathematical Journal, 2004, 56 (11) : 1766 - 1781

← 1 2 3 4 5 →