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Uniqueness and representation theorems for the inhomogeneous heat equation. (English) Zbl 0408.35045


MSC:

35K05 Heat equation
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35C15 Integral representations of solutions to PDEs
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
31C15 Potentials and capacities on other spaces
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References:

[1] Besala, P.; Krzyżaǹski, M., Un théorème d’unicité de la solution du problème de Cauchy pour l’équation linéaire normale parabolique du second ordre, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 33, 230-236 (1962) · Zbl 0114.30003
[2] Brawn, F. T., Positive harmonic majorization of subharmonic functions in strips, (Proc. London Math. Soc., 27 (1973)), 261-289 · Zbl 0265.31008
[3] Friedman, A., Partial Differential Equations of Parabolic Type (1964), Prentice-Hall: Prentice-Hall Englewood Cliffs, N. J · Zbl 0144.34903
[4] Gehring, F. W., The boundary behaviour and uniqueness of solutions of the heat equation, Trans. Amer. Math. Soc., 94, 337-364 (1960) · Zbl 0090.07703
[5] Kuran, Ü., Harmonic majorizations in half-balls and half-spaces, (Proc. London Math Soc., 21 (1970)), 614-636 · Zbl 0207.41603
[6] Nualtaranee, S., On least harmonic majorants in half-spaces, (Proc. London Math. Soc., 27 (1973)), 243-260 · Zbl 0265.31007
[7] Watson, N. A., A theory of subtemperatures in several variables, (Proc. London Math. Soc., 26 (1973)), 385-417 · Zbl 0253.35045
[8] Watson, N. A., Classes of subtemperatures on infinite strips, (Proc. London Math. Soc., 27 (1973)), 723-746 · Zbl 0268.35047
[9] Watson, N. A., Green functions, potentials, and the Dirichlet problem for the heat equation, (Proc. London Math. Soc., 33 (1976)), 251-298 · Zbl 0336.35046
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