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Global Solutions of Coupled Nonlocal Parabolic Systems Arising from Reversible Chemical Reactions

Redouane Douaifia, Salem Abdelmalek, Mokhtar Kirane

Abstract

A class of coupled time-space fractional reaction-diffusion systems derived from reversible chemical reactions over a bounded domain is investigated. Employing mainly an appropriate Lyapunov functional and an improved maximum principle, we demonstrate the global-in-time existence of strong solutions under some assumptions on the systems parameters.

Global Solutions of Coupled Nonlocal Parabolic Systems Arising from Reversible Chemical Reactions

Abstract

A class of coupled time-space fractional reaction-diffusion systems derived from reversible chemical reactions over a bounded domain is investigated. Employing mainly an appropriate Lyapunov functional and an improved maximum principle, we demonstrate the global-in-time existence of strong solutions under some assumptions on the systems parameters.
Paper Structure (6 sections, 9 theorems, 42 equations)

This paper contains 6 sections, 9 theorems, 42 equations.

Table of Contents

  1. Introduction
  2. Main result
  3. Preliminaries
  4. Definitions
  5. Auxiliary Results
  6. Proof of the main result

Key Result

Theorem 1

Let $0<\rho \leq 1$, $\sigma_1,\sigma_2\in (0,1)$, and $u_0,v_0\in C(\Bar{\Omega})$, with $0\leq u_0,v_0\leq \Lambda <+\infty$ for a.e. $x$ in $\Omega$, such that $u_0,v_0\not\equiv 0$. Moreover, let $\lambda\in \{0,1\}$, $(d_u,d_v,k_f,k_b)\in (0,+\infty)^4$, and $(\alpha_i,\beta_i)\in [0,+\infty)^2

Theorems & Definitions (18)

  • Theorem 1
  • Remark 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • ...and 8 more