MR3099032
Sławomir MICHALIK
Sławomir MICHALIK
Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients
Funkcialaj Ekvacioj. Serio Internacia
56
2013
19--50
http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-1/56_19.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3099032
We consider the Cauchy problem for linear moment partial differential equations with constant coefficients in two complex variables. We construct an integral representation of the solution of this problem and study its analyticity. As a result we derive a characterisation of multisummable formal solutions of the Cauchy problem.
Linear PDEs with constant coefficients, Formal power series, Moment functions, Moment PDEs, $k$-summability, Multisummability.
35C10, 35C15, 35E15.
56-19
2013
Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients
Sławomir MICHALIK
Sławomir MICHALIK
1
Balser, W.
Divergent solutions of the heat equation: on an article of Lutz, Miyake and Schäfke
Pacific J. Math.
188
1999
53-63
MR1680415
2
Balser, W.
Formal power series and linear systems of meromorphic ordinary differential equations
Universitext, Springer-Verlag, New York
2000
MR1722871
3
Balser, W.
Multisummability of formal power series solutions of partial differential equations with constant coefficients
J. Differential Equations
201
2004
63-74
MR2057538
4
Balser, W.
Power series solutions of the inhomogeneous heat equation
Recent trends in Microlocal Analysis, Sūrikaisekikenkyūsho Kōkyūroku, No. 1412
2005
pp. 151-159
5
Balser, W.; Duval,A.; Malek, S.
Summability of formal solutions for abstract Cauchy problems and related convolution equations
Ulmer Seminare
11
2006
29-44
6
Balser, W.; Loday-Richaud, M.
Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables
Adv. Dyn. Syst. Appl.
4
2009
159-177
MR2599531
7
Balser, W.; Miyake, M.
Summability of formal solutions of certain partial differential equations
Acta Sci. Math. (Szeged)
65
1999
543-551
MR1737270
8
Balser, W.; Yoshino, M.
Gevrey order of formal power series solutions of inhomogeneous partial differential equations with constant coefficients
Funkcial. Ekvac.
53
2010
411-434
MR2761091
2761091
9
Ichinobe, K.
Integral representation for Borel Sum of Divergent Solution to a Certain Non-Kovalevski Type Equation
Publ. Res. Inst. Math. Sci.
39
2003
657-693
MR2025459
10
Lutz, D. A.; Miyake, M.; Schäfke, R.
On the Borel summability of divergent solutions of the heat equation
Nagoya Math. J.
154
1999
1-29
MR1689170
11
Łysik, G.
Borel summable solutions of the Burgers equation
Ann. Pol. Math.
95
2009
187-197
MR2476613
12
Malek, S.
On the summability of formal solutions of linear partial differential equations
J. Dyn. Control Syst.
11
2005
389-403
MR2147192
13
Michalik, S.
Summability of divergent solutions of the $n$-dimensional heat equation
J. Differential Equations
229
2006
353-366
MR2265631
14
Michalik, S.
Summability of formal solutions to the $n$-dimensional inhomogeneous heat equation
J. Math. Anal. Appl.
347
2008
323-332
MR2433851
15
Michalik, S.
On the multisummability of divergent solutions of linear partial differential equations with constant coefficients
J. Differential Equations
249
2010
551-570
MR2646039
16
Michalik, S.
Summability and fractional linear partial differential equations
J. Dyn. Control Syst.
16
2010
557-584
MR2739017
17
Michalik, S.
Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients
J. Dyn. Control Syst.
18
2012
103-133
MR2902710
18
Michalik, S., Summability of formal solutions of linear partial differential equations with divergent initial data, Manuscript (available on the web page http://www.impan.pl/~slawek/divergent.pdf), 2012
19
Miyake, M.
Borel summability of divergent solutions of the Cauchy problem to non-Kovaleskian equations
Partial Differential Equations and Their Applications (Wuhan, 1999), World Sci. Publ., River Edge, NJ
1999
pp. 225-239
MR1742036