Jong Yeoul Park, Sun Hye Park (2009)
Czechoslovak Mathematical Journal
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We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.
Tian, Lixin, Xu, Ying (2010)
Advances in Difference Equations [electronic only]
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Lopes Frota, Cícero (1994)
Portugaliae Mathematica
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Jong Yeoul Park, Sun Hye Park (2006)
Czechoslovak Mathematical Journal
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We consider the damped semilinear viscoelastic wave equation with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.
Yang, Ying, Yin, Jingxue, Jin, Chunhua (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Tomáš Bárta (2013)
Open Mathematics
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We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.
G. Ströhmer, W. Zajączkowski (1999)
Applicationes Mathematicae
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Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.
Brice Bangola (2013)
Open Mathematics
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We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.