Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source

Carlos Raposo; Adriano Cattai; Octavio Vera; Ganesh Ch. Goraın; Ducival Pereira

doi:10.36753/mathenot.1084371

EN

Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source

Abstract

This manuscript deals with global solution, polynomial stability and blow-up behavior at a finite time for the nonlinear system $$ \left\{ \begin{array}{rcl} & u'' - \Delta_{p} u + \theta + \alpha u' = \left\vert u\right\vert ^{p-2}u\ln \left\vert u\right\vert \\ &\theta' - \Delta \theta = u' \end{array} \right. $$ where $\Delta_{p}$ is the nonlinear $p$-Laplacian operator, $ 2 \leq p < \infty$. Taking into account that the initial data is in a suitable stability set created from the Nehari manifold, the global solution is constructed by means of the Faedo-Galerkin approximations. Polynomial decay is proven for a subcritical level of initial energy. The blow-up behavior is shown on an instability set with negative energy values.

Keywords

Global solution, blow-up, thermoelastic system of p-Laplacian type, logarithmic source

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Carlos Raposo ^*
0000-0001-8014-7499
Brazil

Adriano Cattai
0000-0002-6171-6585
Brazil

Octavio Vera
0000-0001-7304-0976
Chile

Ganesh Ch. Goraın
0000-0002-5326-3635
India

Ducival Pereira
0000-0003-4511-0185
Brazil

Publication Date

September 2, 2023

Submission Date

March 8, 2022

Acceptance Date

July 29, 2022

Published in Issue

Year 2023 Volume: 11 Number: 3

DOI

https://doi.org/10.36753/mathenot.1084371

IZ

https://izlik.org/JA56NW36TC

APA

Raposo, C., Cattai, A., Vera, O., Ch. Goraın, G., & Pereira, D. (2023). Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source. Mathematical Sciences and Applications E-Notes, 11(3), 112-128. https://doi.org/10.36753/mathenot.1084371

AMA

1.Raposo C, Cattai A, Vera O, Ch. Goraın G, Pereira D. Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source. Math. Sci. Appl. E-Notes. 2023;11(3):112-128. doi:10.36753/mathenot.1084371

Chicago

Raposo, Carlos, Adriano Cattai, Octavio Vera, Ganesh Ch. Goraın, and Ducival Pereira. 2023. “Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type With Logarithmic Source”. Mathematical Sciences and Applications E-Notes 11 (3): 112-28. https://doi.org/10.36753/mathenot.1084371.

EndNote

Raposo C, Cattai A, Vera O, Ch. Goraın G, Pereira D (September 1, 2023) Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source. Mathematical Sciences and Applications E-Notes 11 3 112–128.

IEEE

[1]C. Raposo, A. Cattai, O. Vera, G. Ch. Goraın, and D. Pereira, “Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source”, Math. Sci. Appl. E-Notes, vol. 11, no. 3, pp. 112–128, Sept. 2023, doi: 10.36753/mathenot.1084371.

ISNAD

Raposo, Carlos - Cattai, Adriano - Vera, Octavio - Ch. Goraın, Ganesh - Pereira, Ducival. “Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type With Logarithmic Source”. Mathematical Sciences and Applications E-Notes 11/3 (September 1, 2023): 112-128. https://doi.org/10.36753/mathenot.1084371.

JAMA

1.Raposo C, Cattai A, Vera O, Ch. Goraın G, Pereira D. Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source. Math. Sci. Appl. E-Notes. 2023;11:112–128.

MLA

Raposo, Carlos, et al. “Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type With Logarithmic Source”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 3, Sept. 2023, pp. 112-28, doi:10.36753/mathenot.1084371.

Vancouver

1.Carlos Raposo, Adriano Cattai, Octavio Vera, Ganesh Ch. Goraın, Ducival Pereira. Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source. Math. Sci. Appl. E-Notes. 2023 Sep. 1;11(3):112-28. doi:10.36753/mathenot.1084371

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