2019
Том 71
№ 10

All Issues

Burdeina N. O.

Articles: 2
Article (Ukrainian)

Quasilinear hyperbolic stefan problem with nonlocal boundary conditions

Andrusyak R. V., Burdeina N. O., Kirilich V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 9. - pp. 1173–1199

Using the method of contracting mappings, we prove, for small values of time, the existence and uniqueness of a generalized Lipschitz solution of a mixed problem with unknown boundaries for a hyperbolic quasilinear system of first-order equations represented in terms of Riemann invariants with nonlocal (nonseparated and integral) boundary conditions.

Article (Ukrainian)

Classical solvability of a problem with moving boundaries for a hyperbolic system of quasilinear equations

Andrusyak R. V., Burdeina N. O., Kirilich V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 867-891

Using the method of characteristics and the method of contracting mappings, we establish the local classical solvability of a problem for a hyperbolic system of quasilinear first-order equations with moving boundaries and nonlinear boundary conditions. Under additional assumptions on the monotonicity and sign constancy of initial data and a restriction on the growth of the right-hand sides of the system, we formulate sufficient conditions for the global classical solvability of the problem.