Displaying similar documents to “Global solvability of a mixed problem for a nonlinear hyperbolic-parabolic equation in noncylindrical domains.”

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

Albert J. Milani, Hans Volkmer (2011)

Applications of Mathematics

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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 , u ) i 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 , v ) i j v = h . We then give conditions for the convergence, as t , of the solution of the evolution equation to its stationary state.

Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations

B. Eshmatov, E. Karimov (2007)

Open Mathematics

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In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type...