Global solution for a diffusive epidemic model (HIV/AIDS) with an exponential behavior of source

El Hachemi Daddiouaissa

Abstract


We consider the question of global existence and uniform boundedness
of nonnegative solutions of a system of reaction-diffusion equations with
exponential nonlinearity, without any restriction on initial data, using maximum
principle and Lyapunov function techniques.


Keywords


Reaction-diffusion systems; Lyapunov function; global solution.

Full Text:

PDF

References


Alikakos, N., Lp

Di erential Equations, 4(1979), 827-868.

Barabanova, A., On the global existence of solutions of reaction-di usion equation with

exponential nonlinearity, Proc. Amer. Math. Soc., 122(1994), 827-831.

Benachour, S., Rebiai, B., Global classical solutions for reaction-di usion systems with

nonlinearities of exponential growth, J. Evol. Equ., 10(2010), no. 3, 511-527.

Castillo-Chavez, C., Cooke, K., Huang, W., Levin, S.A., On the role of long incubation

periods in the dynamics of acquires immunode ciency syndrome, AIDS, J. Math. Biol.,

(1989), 373-398.

Crandall, M., Pazy, A., Tartar, L., Global existence and boundedness in reaction-di usion

systems, SIAM J. Math. Anal., 18(1987), 744-761.

Cussler, E.L., Di usion, Cambridge University Press, Second Edition, 1997.

Daddiouaissa, E.H., Existence of global solutions for a system of reaction-di usion equa-

tions with exponential nonlinearity, Electron. J. Qual. Theory Di er. Equ., 73(2009), 1-7.

Daddiouaissa, E.H., Global solution for a di usive epidemic model (HIV/AIDS) with a

strong exponential source, Jour. Abstr. Di er. Equ. Appl., 9(2018), no. 1, 30-40.

Djebara, L., Abdelmalek, S., Bendoukha, S., Global existence and asymptotic behavior

of solutions for some coupled systems via Lyapunov functional, Acta Math. Sci. Ser. B.,

B(6)(2019), 1538-1550.

Friedman, A., Partial Di erential Equation of Parabolic Type, Prentice Hall, 1964.

El Hachemi Daddiouaissa

Hamaya, Y., On the asymptotic behavior of a di usive epidemic model (AIDS), Nonlin-

ear Anal., 36(1999), 685-696.

Haraux, A., Kirane, M., Estimation C1 pour des problemes paraboliques semi-lineaires,

Ann. Fac Sci. Toulouse Math., 5(1983), 265-280.

Haraux, A., Youkana, A., On a result of K. Masuda concerning reaction-di usion equa-

tions, Tohoku Math. J., 40(1988), 159-163.

Henry, D., Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math-

ematics 840, Springer-Verlag, New York, 1981.

Hollis, S.L., Martin, R.H., Pierre, M., Global existence and boundedness in reaction-

di usion systems, SIAM J. Math. Anal., 18(1987), no. 3, 744-761.

Kanel, J.I., On global initial boundary-value problems for reaction-di usion systems with

balance conditions, Nonlinear Anal., 37(1999), 971-995.

Kirane, M., Global bounds and asymptotics for a system of reaction-di usion equations,

J. Math Anal. Appl., 138(1989), 1172-1189.

Masuda, K., On the global existence and asymptotic behaviour of reaction-di usion equa-

tions, Hokkaido Math. J., 12(1983), 360-370.

Melkemi, L., Mokrane, A.Z., Youkana, A., Boundedness and large-time behavior results

for a di usive epidemic model, J. Appl. Math., (2007), 1-15.

Pazy, A., Semigroups of Linear Operators and Applications to Partial Di erential Equa-

tions, Springer Verlag, New York, 1983.

Webb, G.F., A reaction-di usion model for a deterministic di usive epidemic, J. Math.

Anal. Appl., 84(1981), 150-161.

Zeidler, E., Nonlinear Functional Analysis and its Applications, Tome II/b, Springer

Verlag, 1990.

Zelenyak, T.I., Stabilization of solutions to boundary value problems for second order

parabolic equations in one space variable, Di er. Uravn. Protsessy Upr., 4(1968), 34-45.




DOI: http://dx.doi.org/10.24193/subbmath.2023.4.15

Refbacks

  • There are currently no refbacks.