Local well-posedness and ill-posedness on the equation of type □u = uk(partial derivativeu)α

被引：9

作者：

Fang, DY ^{[1
]}

Wang, CB ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2005年 / 26卷 / 03期

关键词：

semilinear wave equation; low regularity; local well-posedness; ill-posedness;

D O I：

10.1142/S0252959905000294

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H-s and H-s for semilinear wave equations with polynomial nonlinearity in u and partial derivative u. This ill-posed result concerns the focusing type equations with nonlinearity on u and partial derivative(t)u.

引用

页码：361 / 378

页数：18

共 50 条

[11] On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrodinger equation
Van Duong Dinh
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2018, 25 (03) : 415 - 437
[12] WELL-POSEDNESS AND ILL-POSEDNESS FOR THE CUBIC FRACTIONAL SCHRODINGER EQUATIONS
Cho, Yonggeun
Hwang, Gyeongha
Kwon, Soonsik
Lee, Sanghyuk
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (07) : 2863 - 2880
[13] Well-posedness and ill-posedness for a fifth-order shallow water wave equation
Chen, Wengu
Liu, Zeping
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (05) : 2412 - 2420
[14] On sharp global well-posedness and ill-posedness for a fifth-order KdV-BBM type equation
Carvajal, X.
Panthee, M.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 479 (01) : 688 - 702
[15] Global well-posedness, ill-posedness and long time behavior of solutions of the surface electromigration equation
Zhou, Deqin
NONLINEARITY, 2025, 38 (01)
[16] Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrodinger equation
Bejenaru, I
Tao, T
JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 233 (01) : 228 - 259
[17] SHARP ILL-POSEDNESS AND WELL-POSEDNESS RESULTS FOR THE KdV-BURGERS EQUATION: THE PERIODIC CASE
Molinet, Luc
Vento, Stephane
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (01) : 123 - 141
[18] Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation
Le Dinh Long
Yong Zhou
Rathinasamy Sakthivel
Nguyen Huy Tuan
Journal of Applied Mathematics and Computing, 2021, 67 : 175 - 206
[19] WELL-POSEDNESS AND ILL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE GENERALIZED THIRRING MODEL
Huh, Hyungjin
Machihara, Shuji
Okamoto, Mamoru
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2016, 29 (5-6) : 401 - 420
[20] Well-posedness and ill-posedness results for backward problem for fractional pseudo-parabolic equation
Long, Le Dinh
Zhou, Yong
Sakthivel, Rathinasamy
Tuan, Nguyen Huy
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2021, 67 (1-2) : 175 - 206

← 1 2 3 4 5 →