Relations between travelling wave solutions of quasilinear parabolic equations
HTML articles powered by AMS MathViewer
- by Hans Engler PDF
- Proc. Amer. Math. Soc. 93 (1985), 297-302 Request permission
Abstract:
A transformation between travelling wave solutions of ${v_t} = {v_{xx}} + f\left ( v \right )$ and ${u_t} = {\left ( {D\left ( u \right ){u_x}} \right )_x} + g\left ( u \right )$ is given.References
- Donald G. Aronson, Density-dependent interaction-diffusion systems, Dynamics and modelling of reactive systems (Proc. Adv. Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1979) Publ. Math. Res. Center Univ. Wisconsin, vol. 44, Academic Press, New York-London, 1980, pp. 161–176. MR 588018
- D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978), no. 1, 33–76. MR 511740, DOI 10.1016/0001-8708(78)90130-5
- C. Atkinson, G. E. H. Reuter, and C. J. Ridler-Rowe, Traveling wave solution for some nonlinear diffusion equations, SIAM J. Math. Anal. 12 (1981), no. 6, 880–892. MR 635241, DOI 10.1137/0512074
- Paul C. Fife, Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomathematics, vol. 28, Springer-Verlag, Berlin-New York, 1979. MR 527914 W. S. C. Gurney and R. M. Nisbet, The regulation of inhomogeneous populations, J. Theoret. Biol. 52 (1975), 441-457.
- Morton E. Gurtin and Richard C. MacCamy, On the diffusion of biological populations, Math. Biosci. 33 (1977), no. 1-2, 35–49. MR 682594, DOI 10.1016/0025-5564(77)90062-1
- William I. Newman, Some exact solutions to a nonlinear diffusion problem in population genetics and combustion, J. Theoret. Biol. 85 (1980), no. 2, 325–334. MR 586127, DOI 10.1016/0022-5193(80)90024-7 W. I. Newman and C. Sagan, Galactic civilizations: population dynamics and interstellar diffusion, Icarus 46 (1981), 293-327.
- Joel Smoller, Shock waves and reaction-diffusion equations, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York, 1994. MR 1301779, DOI 10.1007/978-1-4612-0873-0 K. P. Hadeler, Free boundary value problems in biological models, Free Boundary Problems: Theory and Applications (A. Fasano and M. Primicerio, eds.), vol. II, Pitman, Boston, 1983, pp. 664-671.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 297-302
- MSC: Primary 35K55
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770540-6
- MathSciNet review: 770540