Quasilinear hyperbolic stefan problem with nonlocal boundary conditions

Andrusyak, R. V.; Burdeina, N. O.; Kyrylych, V. M.

doi:10.1007/s11253-011-0437-8

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Certain classes of nonlinearities ensuring a nonsingular behavior for autonomous quasilinear systems are described in [13,22]. Some monotonicity and sign preserving conditions on the coefficients of the nonautonomous quasilinear hyperbolic systems are imposed in [1,25]. In the present paper, we study nonautonomous quasilinear hyperbolic systems with lower-order terms and use a different approach focusing on small solutions only.…”

Section: About the Quasilinear System (11)mentioning

confidence: 99%

Bounded and almost periodic solvability of nonautonomous quasilinear hyperbolic systems

Тkachenko

2021

J. Evol. Equ.

View full text Add to dashboard Cite

The paper concerns boundary value problems for general nonautonomous first-order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right-hand sides are small. In the case that all data of the quasilinear problem are almost periodic, we prove that the bounded solution is also almost periodic. For the nonhomogeneous version of a linearized problem, we provide stable dissipativity conditions ensuring a unique bounded continuous solution for any smooth right-hand sides. In the autonomous case, this solution is two times continuously differentiable. In the nonautonomous case, the continuous solution is differentiable under additional dissipativity conditions, which are essential. A crucial ingredient of our approach is a perturbation theorem for general linear hyperbolic systems. One of the technical complications we overcome is the “loss of smoothness” property of hyperbolic PDEs.

show abstract

Section: About the Quasilinear System (11)mentioning

confidence: 99%

Bounded and almost periodic solvability of nonautonomous quasilinear hyperbolic systems

Тkachenko

2021

J. Evol. Equ.

View full text Add to dashboard Cite

show abstract

“…Certain classes of nonlinearities ensuring a non-singular behavior for autonomous quasilinear systems are described in [10,20]. Some monotonicity and sign preserving conditions on the coefficients of the nonautonomous quasilinear hyperbolic systems are imposed in [1,22]. In the present paper, we study nonautonomous quasilinear hyperbolic systems with lower order terms and use a different approach focusing on small solutions only.…”

Section: Comments On the Problem And The Assumptions 121 About The Qu...mentioning

confidence: 99%

Bounded and Almost Periodic Solvability of Nonautonomous Quasilinear Hyperbolic Systems

Kmit,

Recke,

Tkachenko

2019

Preprint

View full text Add to dashboard Cite

We construct small global classical solutions to boundary value problems for nonautonomous quasilinear first-order hyperbolic systems in a strip, assuming that the right hand side is small. We provide stable conditions on the coefficients of the hyperbolic system and on the boundary operator ensuring that the nonhomogeneous version of a linearized problem has a unique bounded classical solution for any smooth right-hand side. We also establish conditions under which this solution smoothly depends on the coefficients of the linearized hyperbolic system. In the case that the data of the problem are almost periodic (respectively, periodic), we prove that the bounded solution is also almost periodic (respectively, periodic).

show abstract

Quasilinear hyperbolic stefan problem with nonlocal boundary conditions

Cited by 2 publications

References 13 publications

Bounded and almost periodic solvability of nonautonomous quasilinear hyperbolic systems

Bounded and almost periodic solvability of nonautonomous quasilinear hyperbolic systems

Bounded and Almost Periodic Solvability of Nonautonomous Quasilinear Hyperbolic Systems

Contact Info

Product

Resources

About