REGULARITY OF WEAK SOLUTIONS OF SEMILINEAR PARABOLIC-SYSTEMS OF ARBITRARY ORDER

被引：4

作者：

GRUNAU, HC ^{[1
]}

VONWAHL, W ^{[1
]}

机构：

[1] UNIV BAYREUTH,LEHRSTUHL ANGEW MATH,W-8580 BAYREUTH,GERMANY

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 1994年 / 62卷

关键词：

D O I：

10.1007/BF02835960

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let u be a weak solution of the initial boundary value problem for the semilinear parabolic system of order 2m : u'(t) + Au(t) + f (t, ., u, ..., del(m)u) = 0. Let f satisfy controllable growth conditions. Then u is smooth. This result is proved by a kind of continuity method, where the time t is the parameter of continuity.

引用

页码：307 / 322

页数：16

共 50 条

[31] Interior C1,γ-regularity for weak solutions of nonlinear second order parabolic systems
Danecek, Josef
John, Oldrich
Stara, Jana
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (07) : 1085 - 1098
[32] LP REGULARITY AND PARTIAL HOLDER CONTINUITY FOR SOLUTIONS OF 2ND ORDER PARABOLIC-SYSTEMS WITH STRICTLY CONTROLLED GROWTH
CAMPANATO, S
ANNALI DI MATEMATICA PURA ED APPLICATA, 1981, 128 : 287 - 316
[33] STATE CONSTRAINED CONTROL-PROBLEMS FOR PARABOLIC-SYSTEMS - REGULARITY OF OPTIMAL-SOLUTIONS
LASIECKA, I
APPLIED MATHEMATICS AND OPTIMIZATION, 1980, 6 (01): : 1 - 29
[34] On the regularity of weak solutions to parabolic systems in two spatial dimensions
John, O
Stara, J
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1998, 23 (7-8) : 1159 - 1170
[35] On regularity of weak solutions to linear parabolic systems with measurable coefficients
Auscher, Pascal
Bortz, Simon
Egert, Moritz
Saari, Olli
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 121 : 216 - 243
[36] AN OPTIMAL REGULARITY RESULT FOR A CLASS OF QUASILINEAR PARABOLIC-SYSTEMS
GIAQUINTA, M
STRUWE, M
MANUSCRIPTA MATHEMATICA, 1981, 36 (02) : 223 - 239
[37] A NOTE ON THE REGULARITY OF AUTONOMOUS QUASILINEAR ELLIPTIC AND PARABOLIC-SYSTEMS
MALY, J
STARA, J
JOHN, O
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1988, 13 (07) : 895 - 903
[38] REGULARITY OF WEAK SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS
邓耀华
李树荣
Science Bulletin, 1986, (08) : 567 - 568
[39] EXISTENCE AND CONTAINMENT OF SOLUTIONS TO PARABOLIC-SYSTEMS
BATES, PW
PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS, 1986, 45 : 103 - 108
[40] SEMILINEAR PARABOLIC-SYSTEMS MODELING SPATIALLY INHOMOGENEOUS EXOTHERMIC REACTIONS
FITZGIBBON, WE
MARTIN, CB
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 178 (01) : 165 - 175

← 1 2 3 4 5 →