Exponential growth of solution of a strongly nonlinear reaction diffusion equation

Authors

  • Hongwei Zhang Henan University of Technology
  • JIng Shu
  • Longfei Qi
  • Qingying Hu

Abstract

An initial boundary value problem for strongly nonlinear reaction diusionequation is studied. We show the exponential growth of solution with Lp- norm using adierential inequalities.

References

Jiang Z., Zheng S. and Song S. Blow-up analysis for a nonlinear diusion equation with nonlinear boundary conditions, Appl. Math. Lett., 17(2004):193-199.

Deng K. and Levine H.A. The role of critical exponents in blow-up theorems: The sequel,

J. Math. Anal. Appl., 243 (2000): 85-126. [3] Levine H.A. Some nonexistence and instability theorems for solutions of formally

parabolic equations of the form Put = ô€€€Au + F(u). Archive for Rational Mechanics and Analysis, 51(1973):371-386.

Kalantarov V.K. and Ladyzhenskaya O.A. The occurrence of collapse for quasilinear

equations of parabolic and hyperbolic type. Journal of Soviet Mathematics, 10(197):53-

Levine H.A., Park S.R and Serrin J.M. Global existence and nonexistence theorems

for quasilinear evolution equations of formally parabolic type. Journal of Dierential

Equations, 142(1998): 212-229.

Messaoudi S.A. A note on blow up of solutions of a quasilinear heat equation with van-

ishing initial energy. Journal of Mathematical Analysis and Applications, 273(2002):243-

Liu W.J. andWang M.X. Blow-up of the solution for a p-Laplacian equation with positive

initial energy. Acta Applicandae Mathematicae, 103(2008): 141-146.

Pucci P. and Serrin J.M. Asymptotic Stability for Nonlinear Parabolic Systems, Energy

Methods in Continuum Mechanics. Kluwer Acad. Publ.: Dordrecht, 1996.

Pang J.S. and Zhang H.W. Existence and nonexistence of the global solution on the

quasilinear parabolic equation. Chin. Quart.J.of Math. 22 (3)(2007): 448-454.

Pang J.S. and Hu Q.Y. Global nonexistence for a class of quasilinear parabolic equa-

tion with source term and positive initial nergy, Journal of Henan University (Natural

Science), 37(5)(2007): 448-451.(in Chinese)

Berrimi S. and Messaoudi S.A. A decay result for a quasilinear parabolic system. Progr.

Nonlinear Dierential Equations Appl, 53(2005):43-50.

Eden A., Michaux B. and Rakotoson J.M. Doubly nonlinear parabolic-type equations as

a dynamical systems, J. Dynamics and Dierential Equations, 3(1)(1991),87-131.

Ouardi H.E. and Hachimi A.E. Attractors for a class of doubly nonlinear parabolic

systems, Electronic J of Qualitative of Dierential Equation, 2006(1)(2006):1-15.

Polat N. Blow up of solution for a nonlinear reaction diusion equation with multiple

nonlinearities, International Journal of Science and Technology,2(2)(2007):123-128.

Korpusov M.O. and Sveshnikov A.G. Sucient close-to-necessary conditions for the

blowup of solution to a strongly nonlinear generalized Boussinesq equation. Compu-

tational Mathematics and Mathematical Physics, 48(9)(2008):1591-1599.

Al'shin A.B., Korpusov M.O. and Sveshnikov A.G. Blowup in Nonlinear Soblev Type

Equation. De Gruyter, Berlin/NewYork, 2011.

S. Gerbi, B. Said-Houari, Local existence and exponential growth for a semilinear

damped wave equation with dynamic boundary conditions, Advances in Dierential

Equations, 13 (2008), 1051-1074.

B. Said-Houari, Exponential growth of positive initial-energy solutions of nonlinear vis-

coelastic wave equations with damping and source term. Z. Angew. Math. Phys. 62

(2011), 115-133.

Vitillaro, E. Global existence theorems for a class of evolution equations with dissipation.

Arch. Ration. Mech. Anal. 149(1999), 155-182.

Asian Journal of Fuzzy and Applied Mathematics (ISSN: 2321 – 564X)

Volume 02 – Issue 05, October 2014

Asian

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Published

2014-10-31

How to Cite

Exponential growth of solution of a strongly nonlinear reaction diffusion equation. (2014). Asian Journal of Fuzzy and Applied Mathematics, 2(5). https://ajouronline.com/index.php/AJFAM/article/view/1250