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Asymptotics in nonlinear evolution system with dissipation and ellipticity on quadrant. (English) Zbl 1107.35026

Summary: We consider an initial boundary value problem for some nonlinear evolution system with dissipation and ellipticity. We establish the global existence and furthermore obtain the \(L^{p}\) \((p\geq 2)\) decay rates of solutions corresponding to diffusion waves. The analysis is based on the energy method and pointwise estimates.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
34B45 Boundary value problems on graphs and networks for ordinary differential equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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