On Equations of the Form Δu - partial derivativeu/partial derivativet = f (x, t, u, Du)

被引：0

作者：

Amanov, R. A. ^{[1
]}

Ismailov, A. I. ^{[2
]}

机构：

[1] Natl Aviat Acad Azerbaijan, Baku, Azerbaijan

[2] Baku State Univ, Baku, Azerbaijan

来源：

AZERBAIJAN JOURNAL OF MATHEMATICS | 2023年 / 13卷 / 02期

关键词：

a priori estimate; semilinear; maximum principle; EXISTENCE;

D O I：

10.59849/2218-6816.2023.2.137

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper describes an interpolation method for obtaining a priori estimates for strong solutions of semilinear parabolic equations with unbounded singularities on the right-hand side, provided that there is a first a priori estimate in the space of summable functions.

引用

页码：137 / 158

页数：22

共 50 条

[21] WEAK SOLUTIONS U(X,T) TO PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS WITH COEFFICIENTS THAT DEPEND UPON U(Y1 ... K,PSI-1 ... K(T,U(X,T)))
CANNON, JR
DUCHATEAU, PC
JOURNAL OF DIFFERENTIAL EQUATIONS, 1981, 42 (03) : 438 - 446
[22] Single-cell fourth-order difference approximations for partial u/ partial x, partial u/ partial y, and partial u/ partial z of the three-dimensional quasi-linear elliptic equation
Mohanty, R.K.
Dey, Shivani
Numerical Methods for Partial Differential Equations, 2000, 16 (05) : 417 - 425
[23] The real solutions of the equation partial derivative(2)u/partial derivative x(2) + partial derivative(2)u/partial derivative y=0
Study, E
MATHEMATISCHE ANNALEN, 1909, 66 : 331 - 336
[24] THE PARTIAL-DIFFERENTIAL EQUATION UT+F(U)X=-CU
HATTORI, H
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 86 (03) : 395 - 401
[25] Local well-posedness and ill-posedness on the equation of type □u = uk(partial derivativeu)α
Fang, DY
Wang, CB
CHINESE ANNALS OF MATHEMATICS SERIES B, 2005, 26 (03) : 361 - 378
[26] NEW RESULTS ON CONTROLLABILITY OF SYSTEMS OF THE FORM X(T)=A(T)X(T)+F(T,U(T))
BARMISH, BR
SCHMITENDORF, WE
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1980, 25 (03) : 540 - 547
[27] Approximation by step functions of functions belonging to Sobolev spaces and uniqueness of solutions of differential equations of the form u" = F(x, u, u′)
Semenova, T. Yu.
IZVESTIYA MATHEMATICS, 2007, 71 (01) : 149 - 180
[28] NUMERICAL-SOLUTION OF PARTIAL-DIFFERENTIAL EQUATIONS - MEIS,T, MARCOWITZ,U
OMODEI, BJ
SEARCH, 1984, 15 (1-2): : 49 - 49
[29] On the nonlinear wave equation u(tt)-u(xx)=f(x,t,u,u(x),u(t)) associated with the mixed homogeneous conditions
Long, NT
Diem, TN
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 29 (11) : 1217 - 1230
[30] 关于方程u_t=△u-f(u（t-τ,x）,u（t,x）)的稳定性
牛培平
兰州大学学报, 1989, (01) : 9 - 16

← 1 2 3 4 5 →