Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put=−Au+ℱ(u)
KeywordsNeural Network Complex System Nonlinear Dynamics Parabolic Equation Electromagnetism
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- 1.Chen, P. J., & M. E. Gurtin, On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19, 614–627 (1968).Google Scholar
- 2.Friedman, A., Partial Differential Equations. New York: Holt, Rinehart, Winston 1969.Google Scholar
- 4.Fujita, H., On the blowing up of solutions to the Cauchy problem for 385-02. J. Faculty Science, U. of Tokyo 13, 109–124 (1966).Google Scholar
- 5.Kaplan, S., On the growth of solutions of quasilinear parabolic equations. Comm. Pure Appl. Math. 16, 305–330 (1963).Google Scholar
- 6.Knops, R. J., & L. E. Payne, Growth estimate for solutions of evolutionary equations in Hubert space with applications in elastodynamics. Arch. Rational Mech. Anal. 41, 363–398 (1971).Google Scholar
- 7.Levine, H. A., Instability and nonexistence of global solutions to nonlinear wave equations of the form Pu tt=-Au+F(u). Trans. Am. Math. Soc. (in press).Google Scholar
- 8.Protter, M. H., Properties of parabolic equations and inequalities. Can. J. Math. 13, 331–345 (1961).Google Scholar
- 9.Protter, M. H., & H. F. Weinberger, Maximum Principles in Differential Equations. Englewood Cliffs, N.J.: Prentice Hall 1967.Google Scholar
- 10.Strauss, W. A., The Energy Method in Nonlinear Partial Differential Equations. Notas de Mathematica No 41. Instituto de Mathematica Pura e Aplicada, Rio de Janeiro (1969).Google Scholar
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