Local existence and global nonexistence of a solution for a Love equation with infinite memory

Zennir, Khaled; Miyasita, Tosiya; Papadopoulos, Pericles

doi:10.1216/jie.2021.33.117

Cited by 4 publications

(2 citation statements)

References 26 publications

(24 reference statements)

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“…The behavior of these substances under rheological tests has been analyzed in many scientific works [3][4][5][6][7][8][9][10], which was firstly proposed by Moore [11] in 1959. All of these scientific works were presented a qualitative explanation of the break down and build-up processes of the structure (For more details, please see earlier studies [12][13][14][15][16][17][18][19]).…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solution for a fractional thixotropic model

Rahai

Slimani

Guesmia

2023

Math Methods in App Sciences

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In this work, we study the existence and uniqueness of solutions of the fractional thixotropic problem in one‐dimensional case. The problem of thixotropic was studied by many researchers. But our study is focussed on the fractional derivative , which is a new addition to the previous works of thixotropic problem. So, in this work, we based on two parts: The first is studding the existence and uniqueness of solutions of the modified fractional thixotropic model using regularization, some prior estimates, and Gronwall's lemma. The second is proving that the problem converges to the fractional thixotropic model by using fixed point theorem.

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Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solution for a fractional thixotropic model

Rahai

Slimani

Guesmia

2023

Math Methods in App Sciences

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“…The question of the well-posedness and spatial regularity of the problem was treated owing to the the theory of evolution process and sectorial operators. Models involving a linear kernel are not new and arise in heat conduction and linear viscoelasticity theory; we mention the works [10][11][12][13][14][15][16][17] and references therein.…”

Section: Introduction Settingmentioning

confidence: 99%

On the Global Nonexistence of a Solution for Wave Equations with Nonlinear Memory Term

Reda,

Memou,

Berkane

et al. 2023

Fractal Fract

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General Decay Rate of Solution for Love-Equation with Past History and Absorption

Zennir

Biomy

2020

Mathematics

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In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love’s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory ϖ in the third section. We found that the system energy decreased according to a very general rate that includes all previous results.

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Local existence and global nonexistence of a solution for a Love equation with infinite memory

Cited by 4 publications

References 26 publications

Existence and uniqueness of solution for a fractional thixotropic model

Existence and uniqueness of solution for a fractional thixotropic model

On the Global Nonexistence of a Solution for Wave Equations with Nonlinear Memory Term

General Decay Rate of Solution for Love-Equation with Past History and Absorption

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