Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators

被引：0

作者：

Biagi, Stefano ^{[1
]}

Punzo, Fabio ^{[1
]}

Vecchi, Eugenio ^{[2
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, ViaBonardi 9, I-20133 Milan, Italy

[2] Univ Bologna, Dipartimento Matemat, Bologna, Italy

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2025年 / 57卷 / 01期

关键词：

BLOW-UP; DIFFUSION-EQUATIONS; HARNACK INEQUALITY; CRITICAL EXPONENTS; HEAT-EQUATION; NONEXISTENCE; ASYMPTOTICS;

D O I：

10.1112/blms.13196

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator L=-Delta+(-Delta)s$\mathcal {L}= -\Delta +(-\Delta)<^>s$, with a power-like source term. We show that the so-called Fujita phenomenon holds, and the critical value is exactly the same as for the fractional Laplacian.

引用

页码：265 / 284

页数：20

共 50 条

[41] Asymptotic behavior of global solutions to a class of mixed pseudo-parabolic Kirchhoff equations
Cao, Yang
Zhao, Qiuting
APPLIED MATHEMATICS LETTERS, 2021, 118 (118)
[42] BLOW-UP OF SOLUTIONS AND EXISTENCE OF LOCAL SOLUTIONS FOR VISCOELASTIC PARABOLIC EQUATIONS
Li, Lanlan
Ye, Yaojun
PROCEEDINGS OF THE ROMANIAN ACADEMY SERIES A-MATHEMATICS PHYSICS TECHNICAL SCIENCES INFORMATION SCIENCE, 2022, 23 (03): : 235 - 244
[43] A priori estimates and existence of positive stationary solutions for semilinear parabolic equations
Zhang, Kaiqiang
Dong, Fangyuan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 542 (01)
[44] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A CLASS OF SEMILINEAR PARABOLIC EQUATIONS WITH BOUNDARY DEGENERACY
Wang, Chunpeng
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (09) : 3125 - 3140
[45] Finite time blow-up and global solutions for a class of semilinear parabolic equations at high energy level
Xu Runzhang
Cao Xiuying
Yu Tao
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (01) : 197 - 202
[46] Global and blow-up solutions for nonlinear parabolic equations with Robin boundary conditions
Ding, Juntang
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 65 (11) : 1808 - 1822
[47] GLOBAL EXISTENCE, EXPONENTIAL DECAY AND BLOW-UP IN FINITE TIME FOR A CLASS OF FINITELY DEGENERATE SEMILINEAR PARABOLIC EQUATIONS
Chen, Hua
Xu, Huiyang
ACTA MATHEMATICA SCIENTIA, 2019, 39 (05) : 1290 - 1308
[48] A sufficient condition for blowup of solutions to a class of pseudo-parabolic equations with a nonlocal term
Zhu, Xiaoli
Li, Fuyi
Liang, Zhanping
Rong, Ting
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (13) : 3591 - 3606
[49] Existence and blow-up of solutions for finitely degenerate semilinear parabolic equations with singular potentials
Xu, Huiyang
COMMUNICATIONS IN ANALYSIS AND MECHANICS, 2023, 15 (02): : 132 - 161
[50] Non-existence of local solutions for semilinear heat equations of Osgood type
Laister, R.
Robinson, J. C.
Sierzega, M.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (10) : 3020 - 3028

← 1 2 3 4 5 →