On the stability of waves of nonlinear parabolic systems

H. Cohen, “Nonlinear Diffusion Problems,” IBM Technical Report. Kolmogorov, 1937, Étude de l'équation de la chaleur avec croissance… et son application à un probléme biologique, Bull. Univ. État Moscou, 6, 1 Peletier, 1969, Asymptotic stability of traveling waves, 418 McKean, 1970, Nagumo's equation, Advances in Math., 4, 209, 10.1016/0001-8708(70)90023-X Lax, 1970, Nonlinear Partial Differential Equations of Evolution, 831 Evans, 1972, Nerve axon equations, I: Linear approximations, Indiana Univ. Math. J., 21, 877, 10.1512/iumj.1972.21.21071 Hodgkin, 1952, A quantitative description of membrane current and its application to conduction and excitation in nerves, J. Physiol., 117, 500, 10.1113/jphysiol.1952.sp004764 Oleinik, 1961, Russian Math. Surveys, 16, 105ff, 10.1070/RM1961v016n05ABEH004114 Conley, 1971, Shock Waves as limits of progressive wave solutions of higher order equations, Comm. Pure Appl. Math., 24, 10.1002/cpa.3160240402 Coddington, 1955 Jeffrey, 1970, Stability of the Burgers shock wave and the Kortewegde Vries soliton, Indiana Univ. Math. J., 20, 463, 10.1512/iumj.1971.20.20039 Evans, 1972, Nerve axon equations, II: Stability at rest, Indiana Univ. Math. J., 22, 75, 10.1512/iumj.1973.22.22009 Evans, 1972, Nerve axon equations, III: Stability of the nerve impulse, Indiana Univ. Math. J., 22, 577, 10.1512/iumj.1973.22.22048 D. H. Sattinger, “Topics in Stability and Bifurcation Theory,” Lecture Notes in Mathematics, No. 309, Springer-Verlag, New York/Berlin. Protter, 1967 Kanel, 1962, On the stability of solutions of the Cauchy problem for equations occurring in the theory of combustion, Mat. Sb., 59, 245 Kanel, 1964, On the stability of solutions of the equations of the theory of combustion for finite initial functions, Mat. Sb., 65, 398 Kanel, 1960, 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 Kanel, 1961, Some problems involving burning-theory equations, DAN SSSR, 136, 277 Gelfand, 1963, Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl., 29, 295, 10.1090/trans2/029/12 Protter, 1966, On the spectrum of general second order operators, Bull. Amer. Math. Soc., 72, 251, 10.1090/S0002-9904-1966-11485-4 Dunford, 1958, Vol. I Riesz, 1955 F. Hoppenstead, “Mathematical Theories of Population,” New York University Lectures Notes. Sattinger, 1975, Stability of Traveling Waves of Nonlinear Parabolic Equations