On a high-order iterative scheme for a nonlinear love equation

Ngoc, Le Thi Phuong; Duy, Nguyen Tuan; Long, Nguyễn Thành

doi:10.1007/s10492-015-0096-4

Cited by 6 publications

(4 citation statements)

References 17 publications

(25 reference statements)

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“…This paper is organized as follows: In the second section, because of the nonlinearities, we combine a three techniques to prove the local existence of unique weak solution in Theorem 2.3. In the third section, the blow up results with negative initial energy is obtained in Theorem 3.3, under certain conditions on the sources and the function g. It is not surprising that this work is inspired from [22], [23], [30], [33].…”

Section: Introductionmentioning

confidence: 99%

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

Zennir¹,

Miyasita²,

Papadopoulos³

2021

J. Integral Equations Applications

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Section: Introductionmentioning

confidence: 99%

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

Zennir¹,

Miyasita²,

Papadopoulos³

2021

J. Integral Equations Applications

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“…Our results are very interesting from an application point of view and, as for as, we know that there is no results for equations of Love waves or Love type waves with the presence of finite/infinite memory term ( [1][2][3][6][7][8][9][10][11][12]).…”

Section: Introductionmentioning

confidence: 99%

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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“…The results are very interesting in the application point of view and, ad for as I know, new that is there is no results for equations of Love waves or Love type waves with the presence of finite/infinite memory term ( [4], [6], [18], [19], [20], [21], [22], [23], [26], [27], . .…”

Section: Introductionmentioning

confidence: 99%