Levine, Howard A. Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\). (English) Zbl 0278.35052 Arch. Ration. Mech. Anal. 51, 371-386 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 339 Documents MSC: 35K55 Nonlinear parabolic equations 35K25 Higher-order parabolic equations 35B99 Qualitative properties of solutions to partial differential equations 35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Chen, P. J., & M. E. Gurtin, On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19, 614–627 (1968). · Zbl 0159.15103 · doi:10.1007/BF01594969 [2] Friedman, A., Partial Differential Equations. New York: Holt, Rinehart, Winston 1969. · Zbl 0224.35002 [3] Friedman, A., Remarks on nonlinear parabolic equations. Proc. Symp. in Appl. Math. AMS 13, 3–23 (1965). · doi:10.1090/psapm/017/0186938 [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). · Zbl 0163.34002 [5] Kaplan, S., On the growth of solutions of quasilinear parabolic equations. Comm. Pure Appl. Math. 16, 305–330 (1963). · Zbl 0156.33503 · doi:10.1002/cpa.3160160307 [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). · Zbl 0227.35017 · doi:10.1007/BF00281873 [7] Levine, H. A., Instability and nonexistence of global solutions to nonlinear wave · Zbl 0288.35003 [8] Protter, M. H., Properties of parabolic equations and inequalities. Can. J. Math. 13, 331–345 (1961). · Zbl 0099.30001 · doi:10.4153/CJM-1961-028-1 [9] Protter, M. H., & H. F. Weinberger, Maximum Principles in Differential Equations. Englewood Cliffs, N.J.: Prentice Hall 1967. · Zbl 0153.13602 [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). · Zbl 0233.35001 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.