Almost automorphic solutions to some classes of partial evolution equations

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations.

[1]  José Paulo Carvalho dos Santos,et al.  Existence results for partial neutral integro-differential equation with unbounded delay , 2007 .

[2]  Gaston M. N'Guérékata,et al.  Topics in Almost Automorphy , 2004 .

[3]  E. H. Morales,et al.  Existence results for partial neutral functional integrodifferential equations with unbounded delay , 2004 .

[4]  Hernán R. Henríquez,et al.  Existence results for partial neutral functional differential equations with unbounded delay , 1998 .

[5]  Toka Diagana,et al.  Existence and uniqueness of pseudo-almost periodic solutions to some classes of semilinear differential equations and applications , 2006 .

[6]  R. Rogers,et al.  An introduction to partial differential equations , 1993 .

[7]  Jin Liang,et al.  Composition of pseudo almost automorphic and asymptotically almost automorphic functions , 2008 .

[8]  Jerome A. Goldstein,et al.  Almost automorphic solutions of semilinear evolution equations , 2004 .

[9]  Gaston M. N’Guérékata,et al.  Existence and Uniqueness of Almost Automorphic Mild Solutions to Some Semilinear Abstract Differential Equations , 2004 .

[10]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[11]  T. Diagana.  Existence and uniqueness of pseudo-almost periodic solutions to some classes of partial evolution equations , 2007 .

[12]  Toka Diagana,et al.  Almost automorphic solutions of evolution equations , 2004 .

[13]  S Bochner,et al.  A NEW APPROACH TO ALMOST PERIODICITY. , 1962, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Hernán R. Henríquez,et al.  Existence of periodic solutions of partial neutral functional differential equations with unbounded delay , 1998 .

[15]  Gaston M. N’Guérékata,et al.  Almost Automorphic and Almost Periodic Functions in Abstract Spaces , 2001 .

[16]  A. Lunardi.  Analytic Semigroups and Optimal Regularity in Parabolic Problems , 2003 .

[17]  G. Folland.  Introduction to Partial Differential Equations , 1976 .