Distributions and heat equation in $SDG$

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1. [1] Artin, M., Grothendieck, A. and Verdier, J.-L., Théorie des Topos (SGA 4), Springer LNM269 (1972). Zbl0234.00007MR354653
2. [2] Chen, K.T.Iterated integrals of differential forms and loop space homology, Annals of Math. (2) 97 (1972), 217-146. Zbl0227.58003MR380859
3. [3] Dubuc, E., Sur les modèles de la géométrie différentielle synthétique, Cahiers de Topologie et Géometrie Diff.20 (1979), 231-279. Zbl0473.18008MR557083
4. [4] Frölicher, A., Cartesian Closed Categories and Analysis of Smooth Maps, in "Categories in Continuum Physics", Buffallo1982 (ed. F.W. Lawvere and S.H. Schanuel), SpringerLecture Notes in Math.1174 (1986). Zbl0601.58015MR842916
5. [5] Frölicher, A., Kriegl, A., Linear Spaces and Differentiation Theory, Wiley1988. Zbl0657.46034MR961256
6. [6] Kelley, J.L., General Topology, Van Nostrand1955. Zbl0066.16604MR70144
7. [7] Kelley, J.L., Namioka, I., and co-authors, Linear Topological Spaces, Van Nostrand1963. Zbl0318.46001MR166578
8. [8] Kock, A.Properties of well-adapted models for synthetic differential geometry, Joum. Pure Appl. Alg.20 (1981), 55-70. Zbl0487.18006MR596153
9. [9] Kock, A., Synthetic Differential Geometry, Cambridge University Press1981. Zbl0466.51008MR649622
10. [10] Kock, A., Calculus of smooth functions between convenient vector spaces, Aarhus Preprint Series 1984/85 No. 18. Retyped in http://home.imf.au.dk/kock/CSF.pdf 
11. [11] Kock, A., Convenient vector spaces embed into the Cahiers topos, Cahiers de Topologie et Géométrie Diff. Catégoriques27 (1986), 3-17. Zbl0596.18005MR845406
12. [12] Kock, A. and Reyes, G.E., Models for synthetic integration theory, Math. Scand.48 (1981), 145-152. Zbl0485.51017MR631331
13. [13] Kock, A. and Reyes, G.E., Corrigendum and addenda to "Convenient vector spaces embed", Cahiers de Topologie et Géométrie Diff. Catégoriques28 (1987), 99-110. Zbl0634.18007MR913966
14. [14] Kock, A. and Reyes, G.E., Some calculus with extensive quantities: wave equation, Theory and Applications of Categories, Vol. 11 (2003), No. 14. Zbl1032.18005MR2005689
15. [15] Kriegl, A. and Michor, P., TheConvenient Setting of Global Analysis, Amer. Math. Soc.1997. Zbl0889.58001MR1471480
16. [16] Lavendhomme, R., Basic Concepts of Synthetic Differential Geometry, Kluwer Acad. Publishers1996. Zbl0866.58001MR1385464
17. [17] Lawvere, F.W., Catgeories of Space and of Quantity, in "The Space of Mathematics. Philosophical, Epistemological and Historical Explorations", DeGruyter, Berlin1992, 14-30. Zbl0846.18001MR1214608
18. [18] Lawvere, F.W., Volterra's Functionals and Covariant Cohesion of Space, Rendiconti del Circolo Mat. di Palermo Serie II, Suppl. 64 (2000), 201-214. Zbl0979.01014MR1785821
19. [19] Losik, M.V.Frechet manifolds as diffeological spaces, Soviet Math. (Iz. vuz)5 (1992), 36-42. Zbl0774.58002MR1213569
20. [20] Moerdijk, I. and and Reyes, G.E., Models for Smooth Infinitesimal Analysis, Springer1991. Zbl0715.18001MR1083355
21. [21] Nel, L.D., Enriched locally convex structures, Differential Calculus and Riesz representations, Joum. Pure Appl. Alg.42 (1986), 165-184. Zbl0608.46045MR857565
22. [22] Porta, H. and Reyes, G.E., Variétés à bord et topos lisse, in "Analyse dans les topos lisses" (ed. G.E. Reyes), Rapport de Rechercehes D.M.S. 80-12, Université de Montréal1980. MR649796
23. [23] Quê, N.V. and Reyes, G.E.Théorie des distribution et théorème d'extension de Whitney, in "Analyse dans les topos lisses" (ed. G.E. Reyes), Rapport de Rechercehes D.M.S. 80-12, Université de Montréal1980. 
24. [24] Reyes, G.E., A model of SDG in which only trivial distributions with compact support have a density, in http://reyes-reyes.com/gonzalo/recent_work/syntheticdifferential/ 
25. [25] Reyes, G.E., Embedding manifolds with boundary in smooth toposes, in http://reyes-reyes.com/gonzalo/recent_work/syntheticdifferential/ [26] Zbl1128.51005
26. [26] Schwartz, L., Théorie des distributions, Tome 1, HermannParis1957. Zbl0037.07301MR209834
27. [27] Schwartz, L., Méthodes mathématiques pour les sciences physiques, HermannParis1961. Zbl0904.35001MR143360
28. [28] Seeley, R.T., Extension of C∞ functions defined in a half space, Proc. Amer. Math. Soc.15 (1964), 625-626. Zbl0127.28403