Solution to nonlinear gradient dependent systems with a balance law
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In this paper, we are concerned with the initial boundary value problem (IBVP) and with the Cauchy problem to the reaction-diffusion system
ut - Δu = -un|∇v|p,
vt - dΔv = un|∇v|p,
where 1 ≤ p ≤ 2, d and n are positive real numbers. Results on the existence and large-time behavior of the solutions are presented.
CitationDahmani, Z., & Kerbal, S. (2007). Solution to nonlinear gradient dependent systems with a balance law. Electronic Journal of Differential Equations, 2007(158), pp. 1-7.
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