Blow-up solution and stability to an inverse problem for a pseudo-parabolic equation

Yaman, Metin

doi:10.1186/1029-242x-2012-274

Cited by 4 publications

(5 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the constant C4 does not depend on m ∈ N. Going back to (26) and considering (27), we obtain another inequality:…”

Section: 1mentioning

confidence: 98%

“…Similar problems were studied in ( [13], [14], [17], [23], [25]), but not for a nonlinear Sobolev type equation. In particular, the solvability of inverse problems with local and non-local redefinition conditions for Sobolev-type equations has been studied in many papers ( [1], [2], [15], [16], [18]- [21], [24], [26]) and in a number of others.…”

mentioning

confidence: 99%

“…Let us consider some works on inverse problems for Sobolev-type equations with an integral overdefinition condition. In [26], we consider the inverse problem for a pseudo-parabolic equation of the form:…”

mentioning

confidence: 99%

See 2 more Smart Citations

An inverse problem for the pseudo-parabolic equation with p-Laplacian

Antont︠s︡ev¹,

Aitzhanov²,

Ashurova³

2022

EECT

View full text Add to dashboard Cite

In this article, we study the inverse problem of determining the right side of the pseudo-parabolic equation with a p-Laplacian and nonlocal integral overdetermination condition. The existence of solutions in a local and global time to the inverse problem is proved by using the Galerkin method. Sufficient conditions for blow-up (explosion) of the local solutions in a finite time are derived. The asymptotic behavior of solutions to the inverse problem is studied for large values of time. Sufficient conditions are obtained for the solution to disappear (vanish to identical zero) in a finite time. The limits conditions that which ensure the appropriate behavior of solutions are considered.

show abstract

“…where the constant C4 does not depend on m ∈ N. Going back to (26) and considering (27), we obtain another inequality:…”

Section: 1mentioning

confidence: 98%

mentioning

confidence: 99%

See 1 more Smart Citation

An inverse problem for the pseudo-parabolic equation with p-Laplacian

Antont︠s︡ev¹,

Aitzhanov²,

Ashurova³

2022

EECT

View full text Add to dashboard Cite

show abstract

“…with the distribution function in the special form h(x) ∶= 𝝎(x) − 𝜘Δ𝝎(x) as in Antontsev et al 2 and Yaman, 3 for pseudoparabolic equations and in Khompysh 4 and Pardeep et al, 5 for Kelvin-Voigt equations, which integrating by parts one can lead to the condition (1.5).…”

Section: Introductionmentioning

confidence: 99%

“…The integral overdetermination condition () can be considered as

\int_{normalΩ} boldv false(boldx, t false) boldh false(boldx false) d boldx = e false(t false), t \geq 0,

with the distribution function in the special form

boldh false(boldx false) : = boldω false(boldx false) - ϰ normalΔ boldω false(boldx false)

as in Antontsev et al 2 and Yaman, 3 for pseudoparabolic equations and in Khompysh 4 and Pardeep et al, 5 for Kelvin–Voigt equations, which integrating by parts one can lead to the condition ().…”

Section: Introductionmentioning

confidence: 99%

An inverse problem for Kelvin–Voigt equations perturbed by isotropic diffusion and damping

Khompysh

Kenzhebai

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we consider an inverse problem of finding a coefficient of right hand side of the following system of Kelvin–Voigt equations perturbed by an isotropic diffusion and damping terms vt+∇π−ϰΔvt−νdiv|D(v)|p−2D(v)=γ|v|m−2v+f(t)g(x,t), divv(x,t)=0. The damping term γ|v|m − 2v in the momentum equation realizes an absorbtion (sink) if γ ≤ 0, and a source if γ > 0. We show how the exponents p, m, the coefficients ν, ϰ, γ, the dimension of the space d, and data of the problem should interact each other for the existence of weak solutions to the problem. We also establish the conditions for uniqueness of the solutions to this problem.

show abstract

Inverse source problem for the pseudoparabolic equation associated with the Jacobi operator

Bekbolat,

Tokmagambetov

2024

Bound Value Probl

View full text Add to dashboard Cite

show abstract

Blow-up solution and stability to an inverse problem for a pseudo-parabolic equation

Abstract: We consider a twofold problem for an inverse problem of pseudo-parabolic equations with a nonlinear term. Sufficient conditions for a blow-up solution are derived and a stability result is established.

Cited by 4 publications

References 6 publications

An inverse problem for the pseudo-parabolic equation with p-Laplacian

An inverse problem for the pseudo-parabolic equation with p-Laplacian

An inverse problem for Kelvin–Voigt equations perturbed by isotropic diffusion and damping

Inverse source problem for the pseudoparabolic equation associated with the Jacobi operator

Contact Info

Product

Resources

About