Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations

Previous Article
Asymptotic stability of singular solution to nonlinear heat equation
DCDS Home
This Issue
Next Article
Index sums of isolated singular points of positive vector fields

September 2009, 25(3): 1003-1032. doi: 10.3934/dcds.2009.25.1003

Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations

1.	Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain

Received July 2008 Revised April 2009 Published August 2009

Abstract
Related Papers

In this paper we give some sharp qualitative and quantitative conditions to guarantee that the exponential type of a linear nonautonomous equation is modified by a linear perturbation. No assumption (periodic, almost periodic, quasi periodic etc) is made on the time behavior of the coefficients of the equation or the perturbation.
The results are applied to the study of the asymptotic behavior, both forwards and pullback, of nonautonomous nonlinear equations.

Keywords: Exponential type, asymptotic behavior, perturbations..

Mathematics Subject Classification: 35B05, 35B20, 35B35, 35K10, 35K55, 35K5.

Citation: A. Rodríguez-Bernal. Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 1003-1032. doi: 10.3934/dcds.2009.25.1003

[1]	Michel Chipot, Senoussi Guesmia. On the asymptotic behavior of elliptic, anisotropic singular perturbations problems. Communications on Pure & Applied Analysis, 2009, 8 (1) : 179-193. doi: 10.3934/cpaa.2009.8.179
[2]	Sanling Yuan, Xuehui Ji, Huaiping Zhu. Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1477-1498. doi: 10.3934/mbe.2017077
[3]	Paola Mannucci, Claudio Marchi, Nicoletta Tchou. Asymptotic behaviour for operators of Grushin type: Invariant measure and singular perturbations. Discrete & Continuous Dynamical Systems - S, 2019, 12 (1) : 119-128. doi: 10.3934/dcdss.2019008
[4]	Seung-Yeal Ha, Yongduck Kim, Zhuchun Li. Asymptotic synchronous behavior of Kuramoto type models with frustrations. Networks & Heterogeneous Media, 2014, 9 (1) : 33-64. doi: 10.3934/nhm.2014.9.33
[5]	Belkacem Said-Houari, Radouane Rahali. Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III. Evolution Equations & Control Theory, 2013, 2 (2) : 423-440. doi: 10.3934/eect.2013.2.423
[6]	Nguyen Huu Du, Nguyen Hai Dang. Asymptotic behavior of Kolmogorov systems with predator-prey type in random environment. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2693-2712. doi: 10.3934/cpaa.2014.13.2693
[7]	Guofu Lu. Nonexistence and short time asymptotic behavior of source-type solution for porous medium equation with convection in one-dimension. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1567-1586. doi: 10.3934/dcdsb.2016011
[8]	Mamoru Okamoto. Asymptotic behavior of solutions to a higher-order KdV-type equation with critical nonlinearity. Evolution Equations & Control Theory, 2019, 8 (3) : 567-601. doi: 10.3934/eect.2019027
[9]	Zhipeng Qiu, Jun Yu, Yun Zou. The asymptotic behavior of a chemostat model. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 721-727. doi: 10.3934/dcdsb.2004.4.721
[10]	Luis Barreira, Liviu Horia Popescu, Claudia Valls. Generalized exponential behavior and topological equivalence. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3023-3042. doi: 10.3934/dcdsb.2017161
[11]	Monica De Angelis, Pasquale Renno. Asymptotic effects of boundary perturbations in excitable systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2039-2045. doi: 10.3934/dcdsb.2014.19.2039
[12]	Mykhailo Potomkin. Asymptotic behavior of thermoviscoelastic Berger plate. Communications on Pure & Applied Analysis, 2010, 9 (1) : 161-192. doi: 10.3934/cpaa.2010.9.161
[13]	Hunseok Kang. Asymptotic behavior of a discrete turing model. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 265-284. doi: 10.3934/dcds.2010.27.265
[14]	Luis Barreira, Claudia Valls. Admissibility versus nonuniform exponential behavior for noninvertible cocycles. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1297-1311. doi: 10.3934/dcds.2013.33.1297
[15]	Meng Liu, Ke Wang. Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2495-2522. doi: 10.3934/dcds.2013.33.2495
[16]	Fioralba Cakoni, Shari Moskow, Scott Rome. Asymptotic expansions of transmission eigenvalues for small perturbations of media with generally signed contrast. Inverse Problems & Imaging, 2018, 12 (4) : 971-992. doi: 10.3934/ipi.2018041
[17]	Pawan Kumar Mishra, Sarika Goyal, K. Sreenadh. Polyharmonic Kirchhoff type equations with singular exponential nonlinearities. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1689-1717. doi: 10.3934/cpaa.2016009
[18]	Fuke Wu, George Yin, Zhuo Jin. Kolmogorov-type systems with regime-switching jump diffusion perturbations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2293-2319. doi: 10.3934/dcdsb.2016048
[19]	Juvencio Alberto Betancourt-Mar, José Manuel Nieto-Villar. Theoretical models for chronotherapy: Periodic perturbations in funnel chaos type. Mathematical Biosciences & Engineering, 2007, 4 (2) : 177-186. doi: 10.3934/mbe.2007.4.177
[20]	Chunpeng Wang. Boundary behavior and asymptotic behavior of solutions to a class of parabolic equations with boundary degeneracy. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 1041-1060. doi: 10.3934/dcds.2016.36.1041

2018 Impact Factor: 1.143

American Institute of Mathematical Sciences