Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents

Lingeshwaran Shangerganesh; Arumugam Gurusamy; Krishnan Balachandran

doi:10.1515/cm-2017-0006

Lingeshwaran Shangerganesh ; Arumugam Gurusamy ; Krishnan Balachandran - Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents

cm:9464 - Communications in Mathematics, June 28, 2017, Volume 25 (2017), Issue 1 - https://doi.org/10.1515/cm-2017-0006

Weak Solutions for Nonlinear Parabolic Equations with Variable ExponentsArticle

Authors: Lingeshwaran Shangerganesh ; Arumugam Gurusamy ; Krishnan Balachandran

In this work, we study the existence and uniqueness of weak solu- tions of fourth-order degenerate parabolic equation with variable exponent using the di erence and variation methods.

https://doi.org/10.1515/cm-2017-0006

Source: HAL:hal-03664941v1

Volume: Volume 25 (2017), Issue 1

Published on: June 28, 2017

Imported on: May 11, 2022

Keywords: [MATH]Mathematics [math]

Licence: Attribution-Non Commercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

13 Documents citing this article

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Alex Kaltenbach, Lecture notes in mathematics, Variable Bochner–Lebesgue Spaces, pp. 43-111, 2023, 10.1007/978-3-031-29670-3_3.

Zengfei Chen;Bingliang Shen, 2023, The Existence of Entropy Solutions for a Class of Parabolic Equations, Mathematics, 11, 17, pp. 3753, 10.3390/math11173753, https://doi.org/10.3390/math11173753.

N. Lakshmipriya;S. Gnanavel;K. Balachandran;Yong-Ki Ma, 2022, Existence and blow-up of weak solutions of a pseudo-parabolic equation with logarithmic nonlinearity, Boundary Value Problems, 2022, 1, 10.1186/s13661-022-01611-3, https://doi.org/10.1186/s13661-022-01611-3.

Sun-Hye Park, 2022, General decay for a viscoelastic von Karman equation with delay and variable exponent nonlinearities, Boundary Value Problems, 2022, 1, 10.1186/s13661-022-01602-4, https://doi.org/10.1186/s13661-022-01602-4.

V. F. Vildanova, 2022, Existence of the Cauchy Problem for Aggregation Equation with Variable Exponents in the Hyperbolic Space, Lobachevskii Journal of Mathematics, 43, 6, pp. 1572-1584, 10.1134/s1995080222090293.

Sun-Hye Park, 2021, Blow-up for a viscoelastic von Karman equation with strong damping and variable exponent source terms, Boundary Value Problems, 2021, 1, 10.1186/s13661-021-01537-2, https://doi.org/10.1186/s13661-021-01537-2.

Tae Gab Ha;Sun‐Hye Park, 2021, Existence and decay results for a von Karman equation with variable exponent nonlinearities, Mathematical Methods in the Applied Sciences, 44, 11, pp. 9475-9486, 10.1002/mma.7372.

Gurusamy Arumugam;André H. Erhardt, 2020, Existence of weak solutions to a certain homogeneous parabolic Neumann problem involving variable exponents and cross-diffusion, Journal of Elliptic and Parabolic Equations, 6, 2, pp. 685-709, 10.1007/s41808-020-00078-6, https://doi.org/10.1007/s41808-020-00078-6.

Gurusamy Arumugam;Jagmohan Tyagi, 2020, Nonnegative solutions to reaction–diffusion system with cross‐diffusion and nonstandard growth conditions, Mathematical Methods in the Applied Sciences, 43, 10, pp. 6576-6597, 10.1002/mma.6401.

Tahir Boudjeriou, 2020, On the diffusion p(x)-Laplacian with logarithmic nonlinearity, Journal of Elliptic and Parabolic Equations, 6, 2, pp. 773-794, 10.1007/s41808-020-00083-9.

Salim A. Messaoudi;Ala A. Talahmeh, 2019, Blow up in a semilinear pseudo-parabolic equation with variable exponents, ANNALI DELL UNIVERSITA DI FERRARA, 65, 2, pp. 311-326, 10.1007/s11565-019-00326-1.

Jamal H. Al-Smail;Salim A. Messaoudi;Ala A. Talahmeh, 2018, Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities, International Journal of Differential Equations, 2018, pp. 1-9, 10.1155/2018/9754567, https://doi.org/10.1155/2018/9754567.

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