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Proceedings of the American Mathematical Society

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Relations between travelling wave solutions of quasilinear parabolic equations

Author: Hans Engler
Journal: Proc. Amer. Math. Soc. 93 (1985), 297-302
MSC: Primary 35K55
MathSciNet review: 770540
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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.

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  • [1] D. G. Aronson, Density-dependent interaction-diffusion systems, Proc. Adv. Sem. on Dynamics and Modeling of Reactive Systems (Madison, 1979), Academic Press, New York, 1980. MR 588018 (82a:35056)
  • [2] D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978), 33-76. MR 511740 (80a:35013)
  • [3] C. Atkinson, G. E. H. Reuter and C. J. Ridler-Rowe, Travelling wave solutions for some nonlinear diffusion equations, SIAM J. Math. Anal. 12 (1981), 880-892. MR 635241 (82k:35058)
  • [4] P. C. Fife, Mathematical aspects of reacting and diffusing systems, Springer-Verlag, Berlin and New York, 1979. MR 527914 (80g:35001)
  • [5] W. S. C. Gurney and R. M. Nisbet, The regulation of inhomogeneous populations, J. Theoret. Biol. 52 (1975), 441-457.
  • [6] M. E. Gurtin and R. C. MacCamy, On the diffusion of biological populations, Math. Biosci. 33 (1977), 35-49. MR 0682594 (58:33147)
  • [7] W. I. Newman, Some exact solutions to a non-linear diffusion problem in population genetics and combustion, J. Theoret. Biol. 85 (1980), 325-334. MR 586127 (82i:92017)
  • [8] W. I. Newman and C. Sagan, Galactic civilizations: population dynamics and interstellar diffusion, Icarus 46 (1981), 293-327.
  • [9] J. Smoller, Shock waves and reaction diffusion equations, Springer-Verlag, Berlin and New York, 1982. MR 1301779 (95g:35002)
  • [10] 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.

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Article copyright: © Copyright 1985 American Mathematical Society

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