W. Balser, Divergent solutions of the heat equation: On an article of Lutz, Miyake and Sch??fke, Pacific Journal of Mathematics, vol.13, issue.1, pp.53-63, 1999.
DOI : 10.1524/anly.1993.13.3.317

W. Balser, Formal power series and linear systems of meromorphic ordinary differential equations, 2000.

W. Balser, Multisummability of formal power series solutions of partial differential equations with constant coefficients, Journal of Differential Equations, vol.201, issue.1, pp.63-74, 2004.
DOI : 10.1016/j.jde.2004.02.002

W. Balser and M. Loday-richaud, Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables, Adv. Dyn. Syst. Appl, vol.4, issue.2, pp.159-177, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00364722

W. Balser and M. Miyake, Summability of formal solutions of certain partial differential equations, Acta Sci. Math. (Szeged), vol.65, pp.3-4543, 1999.

W. Balser and M. Yoshino, Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients, Funkcialaj Ekvacioj, vol.53, issue.3, pp.411-434, 2010.
DOI : 10.1619/fesi.53.411

M. Canalis-durand, J. Ramis, R. Schäfke, and Y. Sibuya, Gevrey solutions of singularly perturbed differential equations, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2000, issue.518, pp.95-129, 2000.
DOI : 10.1515/crll.2000.008

O. Costin, H. Park, and Y. Takei, Borel summability of the heat equation with variable coefficients, Journal of Differential Equations, vol.252, issue.4, pp.3076-3092, 2012.
DOI : 10.1016/j.jde.2011.11.026

M. Hibino, Borel summability of divergent solutions for singular first-order partial differential equations with variable coefficients. Part I, Journal of Differential Equations, vol.227, issue.2, pp.499-563, 2006.
DOI : 10.1016/j.jde.2005.10.001

M. Hibino, On the summability of divergent power series solutions for certain first-order linear PDEs, Opuscula Mathematica, vol.35, issue.5, pp.595-624, 2015.
DOI : 10.7494/OpMath.2015.35.5.595

K. Ichinobe, On k-summability of formal solutions for a class of partial differential operators with time dependent coefficients, Journal of Differential Equations, vol.257, issue.8, pp.3048-3070, 2014.
DOI : 10.1016/j.jde.2014.06.001

A. Lastra and S. Malek, On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems, Journal of Differential Equations, vol.259, issue.10, pp.5220-5270, 2015.
DOI : 10.1016/j.jde.2015.06.020

A. Lastra and S. Malek, On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems, Advances in Difference Equations, vol.53, issue.9, 2015.
DOI : 10.1007/978-1-4612-1506-6

A. Lastra, S. Malek, and J. Sanz, On Gevrey solutions of threefold singular nonlinear partial differential equations, Journal of Differential Equations, vol.255, issue.10, pp.3205-3232, 2013.
DOI : 10.1016/j.jde.2013.07.031

M. Loday-richaud, Stokes phenomenon, multisummability and differential Galois groups, Annales de l???institut Fourier, vol.44, issue.3, pp.849-906, 1994.
DOI : 10.5802/aif.1419
URL : http://archive.numdam.org/article/AIF_1994__44_3_849_0.pdf

M. Loday-richaud, Divergent Series, Summability and Resurgence II. Simple and Multiple Summability, Lecture Notes in Math, vol.2154, 2016.
DOI : 10.1007/978-3-319-29075-1

D. A. Lutz, M. Miyake, and R. Schäfke, Abstract, Nagoya Mathematical Journal, vol.126, pp.1-29, 1999.
DOI : 10.1017/S0027763000004207

S. Malek, On the Summability of Formal Solutions of Linear Partial Differential Equations, Journal of Dynamical and Control Systems, vol.48, issue.3, pp.389-403, 2005.
DOI : 10.1017/S0027763000004207

S. Malek, On Singularly Perturbed Partial Integro-Differential Equations with Irregular Singularity, Journal of Dynamical and Control Systems, vol.325, issue.1, pp.419-449, 2007.
DOI : 10.1016/S0764-4442(97)83928-6

S. Malek, On the Summability of Formal Solutions of Nonlinear Partial Differential Equations with Shrinkings, Journal of Dynamical and Control Systems, vol.7, issue.3, pp.1-13, 2007.
DOI : 10.1155/S1048953302000229

S. Malek, On the Stokes Phenomenon for Holomorphic Solutions of Integro-Differential Equations with Irregular Singularity, Journal of Dynamical and Control Systems, vol.59, issue.60, pp.371-408, 2008.
DOI : 10.1007/978-1-4612-5961-9

S. Malek, On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities, Journal of Dynamical and Control Systems, vol.44, issue.1???2, pp.277-305, 2009.
DOI : 10.1007/BF03322923

S. Malek, On gevrey asymptotics for some nonlinear integro-differential equations, Journal of Dynamical and Control Systems, vol.154, issue.1, pp.377-406, 2010.
DOI : 10.1017/CBO9780511608759

S. Malek, On the summability of formal solutions for doubly singular nonlinear partial differential equations, Journal of Dynamical and Control Systems, vol.7, issue.1, pp.45-82, 2012.
DOI : 10.1016/S0764-4442(97)83928-6

B. Malgrange, Sommation des séries divergentes, Expo. Math, vol.13, pp.163-222, 1995.

B. Malgrange and J. Ramis, Fonctions multisommables, Annales de l???institut Fourier, vol.42, issue.1-2, pp.353-368, 1992.
DOI : 10.5802/aif.1295
URL : http://archive.numdam.org/article/AIF_1992__42_1-2_353_0.pdf

S. Michalik, Summability of divergent solutions of the n-dimensional heat equation, Journal of Differential Equations, vol.229, issue.1, pp.353-366, 2006.
DOI : 10.1016/j.jde.2006.06.005

S. Michalik, On the multisummability of divergent solutions of linear partial differential equations with constant coefficients, Journal of Differential Equations, vol.249, issue.3, pp.551-570, 2010.
DOI : 10.1016/j.jde.2010.03.018

S. Michalik, Summability and fractional linear partial differential equations, Journal of Dynamical and Control Systems, vol.229, issue.4, pp.557-584, 2010.
DOI : 10.1017/S0027763000025289
URL : http://www.ma.utexas.edu/mp_arc/mp_arc/c/09/09-97.pdf

S. Michalik, Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients, Journal of Dynamical and Control Systems, vol.9, issue.1, pp.103-133, 2012.
DOI : 10.1007/s10883-010-9107-7

S. Michalik, Corrigendum to ???On the multisummability of divergent solutions of linear partial differential equations with constant coefficients??? [J. Differential Equations 249 (3) (2010) 551???570], Journal of Differential Equations, vol.255, issue.8, pp.2400-2401, 2013.
DOI : 10.1016/j.jde.2013.06.018

M. Miyake, Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations, Journal of the Mathematical Society of Japan, vol.43, issue.2, pp.305-330, 1991.
DOI : 10.2969/jmsj/04320305

M. Miyake, Borel summability of divergent solutions of the Cauchy problem to non- Kovaleskian equations, Partial differential equations and their applications, pp.225-239, 1999.

M. Miyake and Y. Hashimoto, Newton polygons and gevrey indices for linear partial differential operators, Uber das Anfangswertproblem partieller Differentialgleichungen, pp.15-4741, 1942.
DOI : 10.2977/prims/1195171666
URL : https://www.cambridge.org/core/services/aop-cambridge-core/content/view/58F23F99894A79EDB90357D75414700D/S0027763000004207a.pdf/div-class-title-newton-polygons-and-gevrey-indices-for-linear-partial-differential-operators-div.pdf

S. Ouchi, Multisummability of Formal Solutions of Some Linear Partial Differential Equations, Journal of Differential Equations, vol.185, issue.2, pp.513-549, 2002.
DOI : 10.1006/jdeq.2002.4178

S. Ouchi, Borel summability of formal solutions of some first order singular partial differential equations and normal forms of vector fields, Journal of the Mathematical Society of Japan, vol.57, issue.2, pp.415-460, 2005.
DOI : 10.2969/jmsj/1158242065

M. E. Pli´spli´s and B. Ziemian, Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables, Annales Polonici Mathematici, vol.67, issue.1, pp.31-41, 1997.
DOI : 10.4064/ap-67-1-31-41

J. Ramis, Dévissage Gevrey, pp.59-60173, 1978.

J. Ramis, Les series ?? ??? sommables et leurs applications, Proc. Internat. Colloq., Centre Phys., Les Houches, pp.178-199, 1979.
DOI : 10.1007/3-540-09996-4_38

J. Ramis, Théorèmes d'indices Gevrey pour leséquationsleséquations différentielles ordinaires, Mem. Amer. Math. Soc, vol.48, p.95, 1984.

P. Remy, Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients, Journal of Dynamical and Control Systems, vol.255, issue.10, pp.693-711, 2016.
DOI : 10.1016/j.jde.2013.07.061
URL : https://hal.archives-ouvertes.fr/hal-01171006

P. Remy, Gevrey Order and Summability of Formal Series Solutions of Certain Classes of Inhomogeneous Linear Integro-Differential Equations with Variable Coefficients, Journal of Dynamical and Control Systems, vol.26, issue.10, pp.853-878, 2017.
DOI : 10.2977/prims/1195171666
URL : https://hal.archives-ouvertes.fr/hal-01267736

H. Tahara and H. Yamazawa, Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations, Journal of Differential Equations, vol.255, issue.10, pp.3592-3637, 2013.
DOI : 10.1016/j.jde.2013.07.061

A. Yonemura, Newton polygons and formal Gevrey classes, Publications of the Research Institute for Mathematical Sciences, vol.26, issue.1, pp.197-204, 1990.
DOI : 10.2977/prims/1195171666
URL : http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=26&iss=1&rank=6