Bounds for blow-up time in a semilinear parabolic problem with variable exponents

Abita Rahmoune; Benyattou Benabderrahmane

doi:10.24193/subbmath.2022.1.13

Authors

Abita Rahmoune University Amar Teledji of Laghouat http://orcid.org/0000-0003-2384-2668
Benyattou Benabderrahmane

DOI:

https://doi.org/10.24193/subbmath.2022.1.13

Keywords:

Parabolic equation, Variable nonlinearity, Bounds of the blow-up time.

Abstract

This report deals with a blow-up of the solutions to a class of semilinear
parabolic equations with variable exponents nonlinearities. Under some
appropriate assumptions on the given data, more general lower bounds for a
blow-up time are gained if the solutions blow up. This result extends a
recent results by Baghaei Khadijeh et al. \cite{Baghaei}, which confirms the
Lower bounds for the blow-up time of solutions with initial data $\varphi
\left( 0\right) =\int_{\Omega }u_{0}^{k}dx$, $k$=constant.

Author Biography

Abita Rahmoune, University Amar Teledji of Laghouat

Department of technical sciences, Laghouat university, Algeria.

References

Acerbi, E., Mingione, G., Regularity results for stationary electrorheological fluids, Arch. Ration. Mech. Anal 164 (2002), 213-259.

Antonsev, S.N., Blow-up of solutions to parabolic equations with nonstandard growth conditions, J. Comput. Appl. Math 234 (2010), 2633-2645.

Aiguo, B., Xianfa, S., Bounds for the blowup time of the solutions to quasi-linear parabolic problems, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 65 (2014).

Baghaei, K., Ghaemi, M. B., Hesaaraki, M., Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source, Applied Mathematics Letters 27 (2014).

Ferreira, R., de Pablo, A., Pérez-LLanos, M., Rossi, J. D., Critical exponents for a semilinear parabolic equation with variable reaction, Proceedings of the Royal Society of Edinburgh Section A Mathematics 142 (2012).

Adams, R.A., Sobolev spaces, AP, 1975.

Wang, H., He, Y., On blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy, Applied Mathematics Letters 26 (2013), no. 10, 1008 1012.

Wu, X., Guo, B., Gao, W., Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy, Applied Mathematics Letters 26 (2013).

Abita, R., Upper bound estimate for the blow-up time of a class of integrodifferential equation of parabolic type involving variable source, Comptes Rendus Mathématique 357, (2020), p. 23-32.