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Currently displaying 1 – 3 of 3

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Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.

Albert J. Milani — 1988

Mathematische Zeitschrift

Global existence for quasi-linear dissipative hyperbolic equations with large data and small parameter

Albert J. Milani — 1990

Czechoslovak Mathematical Journal

Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations

Albert J. Milani; Hans Volkmer — 2011

Applications of Mathematics

We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation $u_{t t} + 2 u_{t} - a_{i j} (u_{t}, \nabla u) \partial_{i} \partial_{j} u = f$ corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation $- a_{i j} (0, \nabla v) \partial_{i} \partial_{j} v = h .$ We then give conditions for the convergence, as $t \to \infty$ , of the solution of the evolution equation to its stationary state.

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