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Existence of Positive Solutions and Asymptotic Behavior for Evolutionary q ( x )-Laplacian Equations

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  • Aboubacar Marcos
  • Ambroise Soglo

Abstract

In this paper, we extend the variational method of M. Agueh to a large class of parabolic equations involving q ( x )-Laplacian parabolic equation . The potential is not necessarily smooth but belongs to a Sobolev space . Given the initial datum as a probability density on , we use a descent algorithm in the probability space to discretize the q ( x )-Laplacian parabolic equation in time. Then, we use compact embedding ↪↪ established by Fan and Zhao to study the convergence of our algorithm to a weak solution of the q ( x )-Laplacian parabolic equation. Finally, we establish the convergence of solutions of the q ( x )-Laplacian parabolic equation to equilibrium in the p (.)-variable exponent Wasserstein space.

Suggested Citation

  • Aboubacar Marcos & Ambroise Soglo, 2020. "Existence of Positive Solutions and Asymptotic Behavior for Evolutionary q ( x )-Laplacian Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-23, July.
    • Handle: RePEc:hin:jnddns:9756162
    DOI: 10.1155/2020/9756162
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