Abstract
Any well-posed evolution equation which is not kowalewskian never has the property of finite propagation speed. This property is proved by localizations of operator and energy inequalities.
Similar content being viewed by others
References
L. Gårding,Linear hyperbolic partial differential equations with constant coefficients, Acta Math.85 (1951), 1–62.
L. Hörmander,Pseudo-differential operators and hypoelliptic equations, Proc. Symposium in Singular Integral Operators, Amer. Math. Soc. pp. 138–183.
P. D. Lax and L. Nirenberg,On stability for difference schemes; a sharp form of Gårding’s inequality, Comm. Pure Appl. Math.19 (1966), 473–492.
S. Mizohata,Some remarks on the Cauchy problem, J. of Math., Kyoto Univ.1, (1961) 109–127.
S. Mizohata,On the evolution equations with finite propagation speed, Proc. Japan Acad.46 (1970), 258–261.
L. Schwartz,Théorie des Distributions I.II., 1950–1951.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mizohata, S. On evolution equations with finite propagation speed. Israel J. Math. 13, 173–187 (1972). https://doi.org/10.1007/BF02760236
Issue Date:
DOI: https://doi.org/10.1007/BF02760236