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

[31] Regularity results of solutions to elliptic equations involving mixed local and nonlocal operators
LaMao, CaiDan
Huang, Shuibo
Tian, Qiaoyu
Huang, Canyun
AIMS MATHEMATICS, 2022, 7 (03): : 4199 - 4210
[32] EXPONENTIAL DECAY OF SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS WITH NONLOCAL INITIAL CONDITIONS
DENG, K
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 179 (02) : 630 - 637
[33] SOME MAXIMUM PRINCIPLES FOR PARABOLIC MIXED LOCAL/NONLOCAL OPERATORS
Dipierro, Serena
Lippi, Edoardo proietti
Valdinoci, Enrico
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (09) : 3923 - 3939
[34] Nonlocal solutions of parabolic equations with strongly elliptic differential operators
Benedetti, Irene
Malaguti, Luisa
Taddei, Valentina
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 473 (01) : 421 - 443
[35] Broken and unbroken solutions and dynamic behaviors for the mixed local-nonlocal Schrodinger equation
Yu, Fajun
Liu, Chunping
Li, Li
APPLIED MATHEMATICS LETTERS, 2021, 117
[36] Local and global solutions for some parabolic nonlocal problems
Ianni, Isabella
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (13) : 4904 - 4913
[37] OPTIMAL CONTROL OF MIXED LOCAL-NONLOCAL PARABOLIC PDE WITH SINGULAR BOUNDARY-EXTERIOR DATA
Djida, Jean-Daniel
Mophou, Gisele
Warma, Mahamadi
EVOLUTION EQUATIONS AND CONTROL THEORY, 2022, 11 (06): : 2129 - 2163
[38] Global solutions of abstract semilinear parabolic equations with memory terms
Cannarsa, P
Sforza, D
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2003, 10 (04): : 399 - 430
[39] Global solutions of abstract semilinear parabolic equations with memory terms
Piermarco Cannarsa
Daniela Sforza
Nonlinear Differential Equations and Applications NoDEA, 2003, 10 : 399 - 430
[40] NONEXISTENCE OF GLOBAL-SOLUTIONS TO SYSTEMS OF SEMILINEAR PARABOLIC EQUATIONS
GANG, L
SLEEMAN, BD
JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (01) : 147 - 168

← 1 2 3 4 5 →