Uniqueness of the solution of the Cauchy problem for the partial differential equations and the convolution equations
Abstract
The method of construction of classes of uniqueness of solutions for differential and convolutional equations (containing the classical partial difierential equations) is presented in this paper. It tries to explain the anomaly of uniqueness of solutions for the Laplace and wave equations and non-uniqueness for the equation of heat.
References
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2. J. Mikusiński, Sur la croissance de la fonction operationelle exp(-s^α·λ), Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 7 (1956).
3. A. Tychonoff, Theoremes d'unicite pour l'equation de la chaleur, Mat. Sb. 42, 199-216.
4. M. Piętka, A note on the increase of the operational function exp[λ(Σ_{k=1}^n A_k·s^{p_k})], Ann. Math. Sil. 3 (15) (1989), 107-114.
PiętkaM. (1991). Uniqueness of the solution of the Cauchy problem for the partial differential equations and the convolution equations. Annales Mathematicae Silesianae, 5, 57-67. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14282
Marek Piętka
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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