×

zbMATH — the first resource for mathematics

Well-posedness of the Cauchy problem for some evolution equations. (English) Zbl 0299.35052

MSC:
35K30 Initial value problems for higher-order parabolic equations
35B45 A priori estimates in context of PDEs
35K05 Heat equation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hasegawa, Y., Strongly ^-parabolic systems, Proc. J.A., 37 (1961), 473-477. · Zbl 0106.07103 · doi:10.3792/pja/1195523636
[2] Igari, K., Degenerate parabolic differential equations, Publ. RIMS, Kyoto Univ. 9 (1973) 493-504. · Zbl 0282.35048 · doi:10.2977/prims/1195192569
[3] Mizohata, S., Some remarks on the Cauchy problem, /. Math. Kyoto Univ. 1-1 (1961), 109-127. · Zbl 0104.31903
[4] Mizohata, S., Theory of partial differential equations, Iwanami Tokyo (1965) (in Japanese; will appear in English from Camb. Univ. press).
[5] Nagase, M., On the algebra of a class of pseudo-differential operators and the Cauchy problem for parabolic equations, (to appear). · Zbl 0264.35061
[6] Oleinik, O.A., Linear equations of second order with non-negative form, M. Sbornik, 69 (1966) 111-140, (in Russian), Amer. M.S. Transl., 167-199.
[7] Petrowsky, I. G., Uber das Cauchysche Problem fiir ein System linearer partieller Differentialgleichungen im Gebiete der nichtanalytischen Functionen, Bull, de I’Univ. de VEtat de Moskau, (1938), 1-74. · Zbl 0024.03702
[8] Strang, G., Necessary and insufficient conditions for well-posed Cauchy problems, /. diff. eq., 2 (1966), 107-114. · Zbl 0131.09102 · doi:10.1016/0022-0396(66)90066-0
[9] Takeuchi, J., Thesis for master’s degree, Kyoto Univ. (1969).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.