Duong Trong Luyen, Nguyen Minh Tri (2016)
Annales Polonici Mathematici
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The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator with a locally Lipschitz nonlinearity satisfying a subcritical growth condition.
Albert J. Milani (1990)
Czechoslovak Mathematical Journal
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Mokhtar Kirane, Salim A. Messaoudi (2000)
Revista Matemática Complutense
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We consider a special type of a one-dimensional quasilinear wave equation w - phi (w / w) w = 0 in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.
Nohel, J. A.
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Arkadiusz Szymaniec (2010)
Applicationes Mathematicae
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We consider the initial-value problem for a nonlinear hyperbolic-parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove global (in time) existence and uniqueness of the solution to the initial-value problem for this nonlinear system. The global existence is proved using time decay estimates for the solution of the associated linearized problem. Next, we prove an energy...
Renato Manfrin (1995)
Rendiconti del Seminario Matematico della Università di Padova
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