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Efendiyev, M.A.

Asymptotics of solutions of semilinear elliptic partial differential equations.

Adv. Math. Sci. Appl. 22, 239-258 (2012)

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We consider some elliptic semilinear boundary value problem set either in the quadrant {χ₁ >0} x {χ_N > 0} or in the halfspace {χ₁ >0} if R^N , and we classify the asymptotoc behavior of the solution as χ₁ -> +. The dimension N is taken up to 5 or up to 4, according to the case, and the nonlinearity is of dissipative type. The proof are a combination of techniques borrowed from dynamical systems (to construct a global attractor of solutions) and from partial differential equations (to classify the limit profile of the solutions, to wit the elements of the global attractor).

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