2003, 2003(Special): 563-570. doi: 10.3934/proc.2003.2003.563

Nonlocal problems for quasilinear parabolic equations in divergence form

1. 

Department of Mathematics, Iowa State University, Ames, IA 50011

Received  September 2002 Published  April 2003

We study a class of quasilinear parabolic equations with nonlocal initial conditions. The initial conditions are a generalization of periodicity with respect to time and include conditions studied by other authors, which can be used to study inverse problems and problems arising in reactor theory.
Citation: Gary Lieberman. Nonlocal problems for quasilinear parabolic equations in divergence form. Conference Publications, 2003, 2003 (Special) : 563-570. doi: 10.3934/proc.2003.2003.563
[1]

Pavol Quittner, Philippe Souplet. A priori estimates of global solutions of superlinear parabolic problems without variational structure. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1277-1292. doi: 10.3934/dcds.2003.9.1277

[2]

Tommaso Leonori, Ireneo Peral, Ana Primo, Fernando Soria. Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (12) : 6031-6068. doi: 10.3934/dcds.2015.35.6031

[3]

Xavier Cabré, Manel Sanchón, Joel Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 601-609. doi: 10.3934/dcds.2016.36.601

[4]

Dian Palagachev, Lubomira Softova. A priori estimates and precise regularity for parabolic systems with discontinuous data. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 721-742. doi: 10.3934/dcds.2005.13.721

[5]

Abdelkader Boucherif. Nonlocal problems for parabolic inclusions. Conference Publications, 2009, 2009 (Special) : 82-91. doi: 10.3934/proc.2009.2009.82

[6]

Jianguo Huang, Jun Zou. Uniform a priori estimates for elliptic and static Maxwell interface problems. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 145-170. doi: 10.3934/dcdsb.2007.7.145

[7]

Hui-Ling Li, Heng-Ling Wang, Xiao-Liu Wang. A quasilinear parabolic problem with a source term and a nonlocal absorption. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1945-1956. doi: 10.3934/cpaa.2018092

[8]

Weisong Dong, Tingting Wang, Gejun Bao. A priori estimates for the obstacle problem of Hessian type equations on Riemannian manifolds. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1769-1780. doi: 10.3934/cpaa.2016013

[9]

D. Bartolucci, L. Orsina. Uniformly elliptic Liouville type equations: concentration compactness and a priori estimates. Communications on Pure & Applied Analysis, 2005, 4 (3) : 499-522. doi: 10.3934/cpaa.2005.4.499

[10]

Alfonso Castro, Rosa Pardo. A priori estimates for positive solutions to subcritical elliptic problems in a class of non-convex regions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 783-790. doi: 10.3934/dcdsb.2017038

[11]

Ovidiu Carja, Victor Postolache. A Priori estimates for solutions of differential inclusions. Conference Publications, 2011, 2011 (Special) : 258-264. doi: 10.3934/proc.2011.2011.258

[12]

Ryuichi Suzuki. Universal bounds for quasilinear parabolic equations with convection. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 563-586. doi: 10.3934/dcds.2006.16.563

[13]

Davide Guidetti. Classical solutions to quasilinear parabolic problems with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 717-736. doi: 10.3934/dcdss.2016024

[14]

Zhiqing Liu, Zhong Bo Fang. Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3619-3635. doi: 10.3934/dcdsb.2016113

[15]

Lingwei Ma, Zhong Bo Fang. A new second critical exponent and life span for a quasilinear degenerate parabolic equation with weighted nonlocal sources. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1697-1706. doi: 10.3934/cpaa.2017081

[16]

Marco Cappiello, Fabio Nicola. Sharp decay estimates and smoothness for solutions to nonlocal semilinear equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1869-1880. doi: 10.3934/dcds.2016.36.1869

[17]

Cristina Brändle, Arturo De Pablo. Nonlocal heat equations: Regularizing effect, decay estimates and Nash inequalities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 1161-1178. doi: 10.3934/cpaa.2018056

[18]

Jin Liang, James H. Liu, Ti-Jun Xiao. Nonlocal Cauchy problems for nonautonomous evolution equations. Communications on Pure & Applied Analysis, 2006, 5 (3) : 529-535. doi: 10.3934/cpaa.2006.5.529

[19]

Dian Palagachev, Lubomira G. Softova. Quasilinear divergence form parabolic equations in Reifenberg flat domains. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1397-1410. doi: 10.3934/dcds.2011.31.1397

[20]

Yoshikazu Giga. Interior derivative blow-up for quasilinear parabolic equations. Discrete & Continuous Dynamical Systems - A, 1995, 1 (3) : 449-461. doi: 10.3934/dcds.1995.1.449

 Impact Factor: 

Metrics

  • PDF downloads (1)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]