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Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems

Yong-Fu Yang (2012)

Applications of Mathematics

In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant ${(t, x) : t \geq 0, x \geq 0}$ is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a $C^{1}$ solution and its $L^{1}$ stability with certain small initial and boundary data.

Note on the stability of the Dirichlet problem and the Poisson equation

Petr Pošta (2010)

Acta Universitatis Carolinae. Mathematica et Physica

On the Cauchy problem of a quasilinear degenerate parabolic equation.

Liang, Zongqi, Zhan, Huashui (2009)

Discrete Dynamics in Nature and Society

On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem

Rossitza Semerdjieva (2015)

Open Mathematics

We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.

One-dimensional model describing the non-linear viscoelastic response of materials

Tomáš Bárta (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.