Geodesic
Existence and asymptotic behaviour of solutions of a nonlinear evolution problem
Applications of Mathematics, Tome 42 (1997) no. 6, pp. 411-420

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We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for \begin{align*} ^{\prime\prime} + Au - \Delta u^\prime + |v|^{\rho +2}\,|u|^\rho \,u = f_1\\ ^{\prime\prime} + Av - \Delta v^\prime + |u|^{\rho +2}\,|v|^\rho \,v = f_2 \tag{*}\end{align*} where $A$ is the pseudo-Laplacian operator.
DOI : 10.1023/A:1022251012703
Classification : 34G20, 35A05, 35B40, 35L55, 35L70
Keywords: nonlinear problem; existence of solutions; Galerkin method; compactness; pseudo-Laplacian; asymptotic behaviour; energy type estimates 
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de Oliveira Castro, Nelson Nery. Existence and asymptotic behaviour of solutions of a nonlinear evolution problem. Applications of Mathematics, Tome 42 (1997) no. 6, pp. 411-420. doi: 10.1023/A:1022251012703

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