35K55 | Nonlinear parabolic equations |
35B99 | Qualitative properties of solutions to partial differential equations |
35B35 | Stability in context of PDEs |
[1] | H. Cohen;H. Cohen |
[2] | Kolmogorov, A.; Petrovsky, I.; Piskunov, N., Étude de l’équation de la chaleur avec croissance… et son application à un probléme biologique, Bull. Univ. État Moscou, 6, 1-25 (1937) ·Zbl 0018.32106 |
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[6] | Evans, J. W., Nerve axon equations, I: Linear approximations, Indiana Univ. Math. J., 21, 877-885 (1972) ·Zbl 0235.92002 |
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[8] | Oleinik, O. A.; Kruzhkov, S. N., Russian Math. Surveys, 16, 105ff (1961) |
[9] | Conley, C. C.; Smoller, J., Shock Waves as limits of progressive wave solutions of higher order equations, Comm. Pure Appl. Math., 24 (1971) ·Zbl 0233.35063 |
[10] | Coddington, E. A.; Levinson, N., Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York ·Zbl 0042.32602 |
[11] | Jeffrey, A.; Kakutani, T., Stability of the Burgers shock wave and the Kortewegde Vries soliton, Indiana Univ. Math. J., 20, 463-469 (1970) ·Zbl 0206.11102 |
[12] | Evans, J. W., Nerve axon equations, II: Stability at rest, Indiana Univ. Math. J., 22, 75-90 (1972) ·Zbl 0236.92010 |
[13] | Evans, J. W., Nerve axon equations, III: Stability of the nerve impulse, Indiana Univ. Math. J., 22, 577-593 (1972) ·Zbl 0245.92004 |
[14] | D. H. Sattinger;D. H. Sattinger ·Zbl 0248.35003 |
[15] | Protter, M. H.; Weinberger, H. F., Maximum Principles in Differential Equations (1967), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J ·Zbl 0153.13602 |
[16] | Kanel, Ja. I., On the stability of solutions of the Cauchy problem for equations occurring in the theory of combustion, Mat. Sb., 59, 245-288 (1962) ·Zbl 0152.10302 |
[17] | Kanel, Ja. I., On the stability of solutions of the equations of the theory of combustion for finite initial functions, Mat. Sb., 65, 398-413 (1964) ·Zbl 0168.36301 |
[18] | Kanel, Ja. I., The behavior of solutions of the Cauchy problem when the time tends to infinity, in the case of quasilinear equations arising in the theory of combustion, DAN SSSR, 132, 268-271 (1960) ·Zbl 0152.10301 |
[19] | Kanel, Ja. I., Some problems involving burning-theory equations, DAN SSSR, 136, 277-280 (1961) ·Zbl 0138.35103 |
[20] | Gelfand, I. M., Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl., 29, 295-381 (1963) ·Zbl 0127.04901 |
[21] | Protter, M. H.; Weinberger, H. F., On the spectrum of general second order operators, Bull. Amer. Math. Soc., 72, 251-255 (1966) ·Zbl 0141.09901 |
[22] | Dunford, N.; Schwartz, J. T., (Linear Operators, Vol. I (1958), Interscience: Interscience New York) ·Zbl 0084.10402 |
[23] | Riesz, F.; Sz.-Nagy, B., Functional Analysis (1955), Ungar: Ungar New York |
[24] | F. Hoppenstead;F. Hoppenstead |
[25] | Sattinger, D. H., Stability of Traveling Waves of Nonlinear Parabolic Equations, (Seventh International Conference on Nonlinear Oscillations. Seventh International Conference on Nonlinear Oscillations, East Berlin (1975)) ·Zbl 0359.35038 |