Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About History Editorial Page Addresses Scope Editorial Staff Submission Review For Authors Publication Ethics Issues Русская версия

On an Inequality for Solving Nonlinear Diffusion Equation

Author(s):

Alexander Fedorovich Tedeev

PhD in phisics and mathematics
Assoc.Professor
Dept. of functional analysis and differential equations
K. Khetagurov North-Osetian State University
Vatutin str. 44-46,
362025, Vladikaukaz, RSO-A, Russia

tedeev92@bk.ru

Abstract:

This paper deals with the Cauchy-Dirichlet problem for the nonlinear diffusion equation in the first quadrant with exponential degeneracy on the boundary. The main result of this paper generalizes the Aronson--Benilan inequality, which is then used in obtaining an explicit estimate of solution. The accuracy of the results are confirmed by the examples.

Keywords

References:

  1. Aronson D. G. and Benilan Ph. Regularite des solutions de l'equation des milieux poreus !!!! ERROR!!! IMAGE IS NOT ALLOWERD!. C. R. Acad. Sci. Paris Ser. A-B 288. 1979. P. 103-105
  2. Brezis H. and Grandall M. G. Uniqueness of solutions of the initial-value problem for !!!! ERROR!!! IMAGE IS NOT ALLOWERD!. J. Math. Pures Appl. 1979. Vol. 58. P. 153-163
  3. Grandall M. G. and Pierre M. Regularizing effects for !!!! ERROR!!! IMAGE IS NOT ALLOWERD!. Trans. Amr. Math. Soc. 1982. Vol. 274, № 1
  4. Benilan Ph. and Grandall M. G. The continuous dependence on !!!! ERROR!!! IMAGE IS NOT ALLOWERD! of solutions of !!!! ERROR!!! IMAGE IS NOT ALLOWERD!. Indiana Univ. Math. J. 1981. Vol. 30. P. 162-177
  5. Caffarelli L. A. and Evans L. C. Continuity of the temperature in the two-phase Stefan problem. Arch. Rational Mech. Anal. 1983. Vol. 81, № 3. P. 199-220
  6. Andreucci D. and Tedeev A. F. Large time behavior for the porous medium equation with convection. Meccanica, New Thends in Dynamic and Stability. 2017. P. 1-11
  7. Tedeev Al. F. [Local properties of solutions of the Cauchy problem for a second-order quasilinear parabolic equation] Vladikavkazskij matematicheskij zhurnal. 2008. Vol. 10, № 2. P. 46-57. (in Russ. )
  8. Tedeev Al. F. [The property of a finite velocity of propagation of disturbances for solving the Dirichlet problem of the differential equation of inhomogeneous diffusion] Differencial'nye uravnenija i processy upravlenija. 2016. № 4. P. 93-131. (in Russ. )
  9. Tedeev Al. F., Shelepov V. Ju. [On an inequality for solutions of elliptic equations and its application in the theory of boundary properties] Doklady AN SSSR. 1992. Vol. 315, № 1. P. 40-43. (in Russ. )
  10. Ladyzhenskaja O. A., Solonnikov V. A., Ural'ceva N. N. Linejnye i kvazilinejnye uravnenija parabolicheskogo tipa [Linear and quasilinear equations of parabolic type]. Moscow, 1967. 736 p. (in Russ. )

Full text (pdf)