Dirichlet problem with degeneration of the input data on the boundary of the domain

Rukavishnikov, V. A.; Rukavishnikova, Elena I.

doi:10.1134/s0012266116050141

Cited by 9 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The indicated type of degeneracy raises many new and open questions related to the well-posedness of the hyperbolic equations in suitable functional spaces. It should be emphasized here that boundary value problems for degenerate elliptic and parabolic equations have received a lot of attention in the last years (see, for instance, [5,6,[16][17][18]). In the meantime, as for the control issue for degenerate wave equations, we can mention only a few recent publications [2,3,11], where the authors mainly deal with weakly or strongly degenerate wave equations for which the degeneracy zone is located at a boundary point.…”

Section: Presentation Of the Problemmentioning

confidence: 99%

On an Initial Boundary-Value Problem for 1d Hyperbolic Equation With Interior Degeneracy: Series Solutions With the Continuously Differentiable Fluxes

Borsch

Kogut

Leugering³

2020

JODEA

View full text Add to dashboard Cite

show abstract

Section: Presentation Of the Problemmentioning

confidence: 99%

On an Initial Boundary-Value Problem for 1d Hyperbolic Equation With Interior Degeneracy: Series Solutions With the Continuously Differentiable Fluxes

Borsch

Kogut

Leugering³

2020

JODEA

View full text Add to dashboard Cite

show abstract

“…Hence, new tools are necessary for the analysis of the corresponding optimal control problems. It should be emphasized here that boundary value problems for degenerate elliptic and parabolic equations have received a lot of attention in the last years (see, for instance, literature 6,[10][11][12][13][14]15 ). As for the control issue for degenerate wave equations, we already mentioned 2,16 (see also Lasiecka and Sokolowski 17 for the sensitivity analysis of optimal control problems for wave equations in domain with defects).…”

Section: Introductionmentioning

confidence: 99%

On boundary exact controllability of one‐dimensional wave equations with weak and strong interior degeneration

Kogut

Kupenko

Leugering

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well‐posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions. Passing to a relaxed version of the original problem, we discuss existence and uniqueness of solutions, and using the HUM method we derive conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof.

show abstract

“…Hence, new tools are necessary for the analysis of the corresponding optimal control problems. It should be emphasized here that boundary value problems for degenerate elliptic and parabolic equations have received a lot of attention in the last years (see, for instance, [5,6,9,23,24,26]). As for the control issue for degenerate wave equations, we already mentioned [1,14] (see also [20] for the sensitivity analysis of optimal control problems for wave equations in domain with defects).…”

Section: Introductionmentioning

confidence: 99%

On Boundary Exact Controllability of One-Dimensional Wave Equations with Weak and Strong Interior Degeneration

Kogut,

Kupenko,

Leugering

2021

Preprint

View full text Add to dashboard Cite

In this paper we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well-posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions. Passing to a relaxed version of the original problem, we discuss existence and uniqueness of solutions, and using the HUM method we derive conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof.

show abstract

Dirichlet problem with degeneration of the input data on the boundary of the domain

Cited by 9 publications

References 6 publications

On an Initial Boundary-Value Problem for 1d Hyperbolic Equation With Interior Degeneracy: Series Solutions With the Continuously Differentiable Fluxes

On an Initial Boundary-Value Problem for 1d Hyperbolic Equation With Interior Degeneracy: Series Solutions With the Continuously Differentiable Fluxes

On boundary exact controllability of one‐dimensional wave equations with weak and strong interior degeneration

On Boundary Exact Controllability of One-Dimensional Wave Equations with Weak and Strong Interior Degeneration

Contact Info

Product

Resources

About