$({\mathrm R},{\mathcal B})$-Multidimensional-almost automorphic functions with applications to integral and partial differential equations

In this paper, we analyze the classes of (R,B)-multi-almost automorphic functions and asymptotically (R,B)-multi-almost automorphic functions. We provide plenty valuable applications to the abstract Volterra integrodifferential equations in Banach spaces and partial differential equations.

[1]  Discontinuous almost periodic type functions, almost automorphy of solutions of differential equations with discontinuous delay and applications , 2014 .

[2]  Compact almost automorphic solutions for some nonlinear integral equations with time-dependent and state-dependent delay , 2017 .

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

[4]  Syed Abbas.  A note on Weyl pseudo almost automorphic functions and their properties , 2012 .

[5]  M. Kostic,et al.  Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents , 2020, Mathematics.

[6]  John von Neumann,et al.  On Compact Solutions of Operational-Differential Equations. I , 1935 .

[7]  W. Veech,et al.  Almost Automorphic Functions on Groups , 1965 .

[8]  Sean McKee,et al.  An Euler-type method for two-dimensional Volterra integral equations of the first kind , 2000 .

[9]  R. Ortega,et al.  Almost periodic linear differential equations with non-separated solutions , 2006 .

[10]  Goong Chen,et al.  Control and Stabilization for the Wave Equation in a Bounded Domain , 1979 .

[11]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[12]  R. Grimmer.  Resolvent operators for integral equations in a Banach space , 1982 .

[13]  Zhinan Xia.  Pseudo Asymptotic Behavior of Mild Solution for Nonautonomous Integrodifferential Equations with Nondense Domain , 2014, J. Appl. Math..

[14]  Wei Lin,et al.  Square-mean weighted pseudo almost automorphic solutions for non-autonomous stochastic evolution equations , 2013 .

[15]  G. N’Guérékata,et al.  EXISTENCE OF ASYMPTOTICALLY ALMOST AUTOMORPHIC MILD SOLUTIONS FOR NONAUTONOMOUS SEMILINEAR EVOLUTION EQUATIONS , 2018 .

[16]  Mehdi Dehghan,et al.  A meshless local discrete Galerkin (MLDG) scheme for numerically solving two-dimensional nonlinear Volterra integral equations , 2019, Appl. Math. Comput..

[17]  Samuel Zaidman,et al.  Almost-periodic functions in abstract spaces , 1985 .

[18]  乔花玲,et al.  关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解 , 2003 .

[19]  N. Wiener,et al.  Almost Periodic Functions , 1932, The Mathematical Gazette.

[20]  Y. Sibuya.  Almost periodic solutions of Poisson’s equation , 1971 .

[21]  P. Falb.  On a theorem of Bochner , 1969 .

[22]  Toka Diagana,et al.  Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces , 2013 .

[23]  Yingfei Yi,et al.  Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows , 1998 .

[24]  M. Kostic.  Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations , 2019 .

[25]  Discontinuous Almost Automorphic Functions and Almost Automorphic Solutions of Differential Equations with Piecewise Constant Argument , 2013, 1306.0922.

[26]  J. H. Smith.  Methods of Mathematical Physics, Volume II, Partial Differential Equations , 1963 .

[27]  Richard K. Miller.  On almost periodic differential equations , 1964 .

[28]  R. Nagel,et al.  One-parameter semigroups for linear evolution equations , 1999 .

[30]  J. Prüss.  Evolutionary Integral Equations And Applications , 1993 .

[31]  B. Es-sebbar.  Almost automorphic evolution equations with compact almost automorphic solutions , 2016 .

[32]  Jin Liang,et al.  Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications , 2009 .

[33]  P. Milnes.  Almost automorphic functions and totally bounded groups , 1977 .

[34]  Jin Liang,et al.  Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions , 2008 .

[35]  Pseudo almost automorphic mild solution of nonautonomous stochastic functional integro-differential equations , 2018 .

[36]  A. Reich.  Präkompakte gruppen und fastperiodizität , 1970 .

[37]  K. Ezzinbi,et al.  Almost automorphic solutions for nonautonomous parabolic evolution equations , 2019, Semigroup Forum.

[38]  Zhanrong Hu,et al.  Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain , 2013 .

[39]  S. Bochner.  UNIFORM CONVERGENCE OF MONOTONE SEQUENCES OF FUNCTIONS. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Russell Johnson.  A linear, almost periodic equation with an almost automorphic solution , 1981 .

[41]  Siraj-ul-Islam,et al.  A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations , 2014, J. Comput. Appl. Math..

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