Displaying similar documents to “Initial-boundary value problem in nonlinear hyperbolic thermoelasticity. Some applications in continuum mechanics”

Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body

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...

Well Posedness of Balance Laws with Non-Characteristic Boundary

Rinaldo M. Colombo, Massimiliano D. Rosini (2007)

Bollettino dell'Unione Matematica Italiana

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This note presents a well posedness result for the initial-boundary value problem consisting of a nonlinear system of hyperbolic balance laws with boundary, in the non-characteristic case.

Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations

Yoshihiro Shibata (1993)

Commentationes Mathematicae Universitatis Carolinae

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The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.