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Some properties of solutions for semilinear heat equations with timelag. (English) Zbl 0314.35051


MSC:

35K55 Nonlinear parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
35A15 Variational methods applied to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
35C15 Integral representations of solutions to PDEs
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References:

[1] Fujita, H.: On the blowing up of solutions of the Cauchy problem for \(ut = {\delta}u + u1 + {\alpha}\). J. fac. Sci. univ. Tokyo sect. I part 2 13, 109-124 (1966) · Zbl 0163.34002
[2] Fujita, H.: On some non-existence and non-uniqueness theorems for non-linear parabolic equations. Proceedings of the of American math. Symposium on non-linear functional analysis (April 1968)
[3] Hale, J.: Functional differential equations. Appl. math. Sciences 3 (1971) · Zbl 0222.34003
[4] K. Kobayashi, T. Sirao, and H. Tanaka, On the growing up problem for semi-linear heat equations, to appear. · Zbl 0353.35057
[5] Lions, J. L.: Quelques methods de résolution des problèmes aux limites non-linéaire. (1969) · Zbl 0189.40603
[6] Lions, J. L.; Magenes, E.: Problèmes aux limites non-homogènes et applications. 1 (1968) · Zbl 0165.10801
[7] Lions, J. L.; Magenes, E.: Problèmes aux limites non-homogènes et applications. 2 (1968) · Zbl 0165.10801
[8] Segal, I. E.: Dispersion for non-linear relativistic equations II. Ann. ecol. Norm. sup. 1, 459-497 (1968) · Zbl 0179.42302
[9] Sobolev, S. L.: Applications of functional analysis in mathematical physics. Amer. math. Soc. transl. Of math. Monographs. 7 (1963) · Zbl 0123.09003
[10] Travis, C. C.; Webb, G. F.: Existence and stability for partial functional differential equations. Trans. amer. Math. soc. 200, 395-418 (1974) · Zbl 0299.35085
[11] Wang, P. K. G: Optimal control of parabolic systems with boundary conditions involving time delays. SIAM J. Control 13, 274-293 (1975) · Zbl 0301.49009
[12] Wang, P. K. G: Asymptotic stability of a diffusion system with time-delays. J. appl. Mech. ser. E 30, 500-504 (1963) · Zbl 0137.08003
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