Integral type Cauchy problem for abstract wave equations and applications

Agarwal, Ravi P.; Shakhmurov, Veli

doi:10.1080/00036811.2021.2021184

Cited by 2 publications

(2 citation statements)

References 35 publications

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“…in [23][24][25][26][27][28][29][30][31][32]. This paper generalises the results obtained in [26] and [32] because the general elliptic operator is involved instead of the Laplace operator in the leading part of the equation. The L p well-posedness of the integral problem (1.1) − (1.2) depends crucially on interpolation spaces that data functions belong, the presence of the linear operators L, A and nonlinear operator f (u).…”

Section: Introduction Denitions and Backgroundsupporting

confidence: 56%

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Regularity properties of integral problems for wave equations and applications

Shakhmurov

Shahmurov

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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In this paper, the integral problem for linear and nonlinear wave equations are studied.The equation involves elliptic operator L and abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data given in corresponding interpolation spaces and operators the existence, uniqueness, L^{p}-regularity properties to solutions are established. By choosing the space H and operators L, A, the regularity properties to solutions of different classes of wave equations in the field of physics are obtained.

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Section: Introduction Denitions and Backgroundsupporting

confidence: 56%

“…The abstract equations were studied e.g. in [23][24][25][26][27][28][29][30][31][32]. This paper generalises the results obtained in [26] and [32] because the general elliptic operator is involved instead of the Laplace operator in the leading part of the equation.…”

Section: Introduction Denitions and Backgroundmentioning

confidence: 72%

Regularity properties of integral problems for wave equations and applications

Shakhmurov

Shahmurov

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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Non‐instantaneous impulsive Riemann–Liouville fractional differential systems: Existence and controllability analysis

Sahijwani

Sukavanam

Haq

2023

Math Methods in App Sciences

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The article is dedicated towards the study of fractional order nonlinear differential systems with non‐instantaneous impulses involving Riemann–Liouville derivatives with fixed lower limits and appropriate integral type initial conditions in Banach spaces. First, a mild solution of the system is constructed, and subsequently, its existence is proven using Banach's fixed point theorem. Then, results of approximate controllability are established using the concept of fractional semigroup and an iterative technique. Suitable examples are given in the end supporting the methodology along with pointing out corrections in examples presented in previous articles.

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Integral type Cauchy problem for abstract wave equations and applications

Cited by 2 publications

References 35 publications

Regularity properties of integral problems for wave equations and applications

Regularity properties of integral problems for wave equations and applications

Non‐instantaneous impulsive Riemann–Liouville fractional differential systems: Existence and controllability analysis

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