Díaz Díaz, Jesús Ildefonso2023-06-202023-06-202012Benilan, Ph. and Díaz, J.I. (2004) ‘Pointwise gradient estimates of solutions of onedimensional nonlinear parabolic problems’, J. Evolution Equations, Vol. 3,pp.557–602. Diaz, J.I. (2012) ‘On some onedimensional parabolic reaction-diffusion-convection equations’, Journal of Mathematical Analysis and Applications, to appear. Díaz, J.I. and Kamin, S. (2012) ‘Convergence to travelling waves for quasilinear fisher-KPP type equations’, Journal of Mathematical Analysis and Applications, to appear. DiBenedetto, E. (1983) ‘Continuity of weak solutions to a general porous medium equation’,Indiana Univ. Math. J., Vol. 32, No. 1, pp.83–118. Fisher, R.A. (1937) ‘The wave of advance of advantageous genes’, Annals of Eugenics, Vol. 7, pp.355–369. Gilding, B.H. (1976) ‘Hölder continuity of solutions of parabolic equations’, J. London Math. Soc., Vol. s2-13, No. 1, pp.103-106. Kalashnikov, A.S. (1974) ‘The propagation of disturbances in problems of non-linear heat conduction with asorption’, USSR Comput. Math. and Math. Phys., Vol. 14, pp.70–85. Kamin, S. and Rosenau, P. (2004) ‘Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation’, Rendiconti Mat. Acc. Lincei Cl. Sci. Fis. Mat. Natur., Vol. 15, pp.271–280. Kersner, R. (1984) ‘Degenerate parabolic equations with general nonlinearities’, Nonlinear Anal., Vol. 4, pp.1043–1062. Kolmogorov, A., Petrovsky, I. and Piscunov, N. (1937) Etude de l’equation de la diffusion avec croissance de la quantité de matiere et son application a un probleme biologique,Bulletin Univ. Moscow, Ser. Internationale, Math., Mec., in Pelce, P. (Ed.), Vol. 1, pp.1–25. English translation, Dynamics of Curved Fronts, Academic Press, Boston, 1988,pp.105–130. Kruzhkov, S.N. (1969) ‘Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications’, Math. Zam. English tr. in Math. Notes V, Vol. 6, No. 1, pp.97–98, pp.517–523. Ladyzenskaya, O.A., Solonnikov, V.A. and Ural’tseva, N.N. (1968) Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, Vol. 23,Amer. Math. Soc, Providence, RI. Oleinik, O.A., Kalashnikov, A.S. and Chzhou, Y-L. (1958) ‘The Cauchy problem and boundary problems for equations of the type of nonstationary filtration’, Izv. Akad.Nauk. SSSR Ser. Mat, Vol. 22, pp.667–704 (Russian).1752-3583https://hdl.handle.net/20.500.14352/44514We prove a pointwise gradient estimate for the solution of the Cauchy problem associated to the quasilinear Fisher-KPP type equation with a diffusion coefficient ϕ(u) satisfying that ϕ(0) = 0, ϕ(1) = 1 and a source term ψ(u) which is vanishing only for levels u = 0 and u = 1. As consequence we prove that the bounded weak solution becomes instantaneously a continuous function even if the initial datum is merely a bounded function.engjournal articlehttp://inderscience.metapress.com/content/k376h50312414g61/fulltext.pdfhttp://inderscience.metapress.com/restricted access519.9Gradient estimatesquasilinear Fisher-KPP type equationsregularising effectsspatial uniformation.Ecuaciones diferenciales1202.07 Ecuaciones en Diferencias