Gronwall's Vector Inequality and its Application to a Class of Non-Self-Adjoint Linear and Non-Linear Hyperbolic Partial Differential Equations

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Authors

  • Princeton University, Princeton, N.J. ,US
  • 16/1. Loudan St., Calcutta 17 ,IN

Abstract

Stimulating research works have been undertaken ([1], [2], [5], [6], [8], [10]) to generalize the original form of Gronwall's inequality [3], [7] due to its importance in the study of differential equations. The works done so far, can be employed to investigate different properties of ordinary differential equations and some self-adjoint [8] partial differential equations of hyperbolic type. However, our work [5] is applicable to non-self adjoint cases in two dimensions.

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Published

1974-12-01

How to Cite

Ghoshal, S. K., & Abu Masood, M. (1974). Gronwall’s Vector Inequality and its Application to a Class of Non-Self-Adjoint Linear and Non-Linear Hyperbolic Partial Differential Equations. The Journal of the Indian Mathematical Society, 38(1-4), 383–394. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/16715

 

References

BEHARI. I: A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations: Acta Math, Acd. Sci. Hung,! (1956), 81-94.

. BELLMAN, R: Duke Math. J. 10 (1943), 643-647.

BRAUER, F. AND NOHEL. J.A: Qualitative Theory of Ordinary Differential Equations”Benjamin 1969.

GARABEDIAN P.R.: Partial Differential Equations Chap.”4, pp. 127-134, Joha Wiley and Sons.

GHOSHAL, S. AND MASOOD, M. A.: Generalized Gronwall's inequality and its applications to non-self adjoint linear and non-linear hyperbolic partial differential equations: Journal of Pure and Appl. Maths. National Academy of Sciences, New Delhi, India. (In the Press)

GHOSHAL, S. AND MASOOD M. A.: Generalized n-dimensional Gronwall's inequality and its applications”Accepted for publication in Annates Pol. Math.

GIULIANO, L: Generalizations di un lemma di Gronwall's di una disuguagalianzo di peano, Rend. Ace. Naz. Lincei, (8), 1 (1946), 1264-1271.

GRONWAIX, T.H.: Ann. Math. Sec-2. 20 (1919), 292-296.

SNOW, D.R.: Gronwall's inequality for systems of partial differential equations in two independent variables”Proc. American Math. Soc.

WALTER, W: Differential und Integral Ungleichungen, Springer-Verlag (1964) 125-126.

WEYL.H: Concerning a classical problem in the theory of singular points of ordinary differential equations”Revista de CienciasLima, 46 (1944) 70-112.