Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation
Authors:
Article info
2011-06-15
2012-02-12
2012-02-12
19 - 42
Keywords
Abstract
In this work, we are going to study under some conditions on p, m and suitable conditions on g, the decay of solutions of the nonlinear viscoelastic hyperbolic equation in problem (P) as t : (P) Where Ω is a bounded domain in RN (N>1), with smooth boundary Γ, and a, b, w are positive constants, m≥2, p≥2, and the function g(t) satisfying some conditions. We show that the energy of solutions decays exponentially if m=2 and polynomial if m>2, provided that the initial data are small enough.
Zennir, K. (2012). Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation. An-Najah University Journal for Research - A (Natural Sciences), 26(1), 19–42. https://doi.org/10.35552/anujr.a.26.1.95
[1]K. Zennir, “Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation,” An-Najah University Journal for Research - A (Natural Sciences), vol. 26, no. 1, pp. 19–42, Feb. 2012, doi: 10.35552/anujr.a.26.1.95.
Zennir, Khaled. “Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation.” An-Najah University Journal for Research - A (Natural Sciences), vol. 26, no. 1, Feb. 2012, pp. 19–42. Crossref, https://doi.org/10.35552/anujr.a.26.1.95.
1.Zennir K. Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2012 Feb;26(1):19–42. Available from: http://dx.doi.org/10.35552/anujr.a.26.1.95
Zennir, Khaled. “Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation.” An-Najah University Journal for Research - A (Natural Sciences) 26, no. 1 (February 2012): 19–42. https://doi.org/10.35552/anujr.a.26.1.95.
سلوك حلول المعادلات التفاضلية الجزئية الزائدية غير الخطية بوجود دالة الذاكرة
المؤلفون:
معلومات المقال
2011-06-15
2012-02-12
2012-02-12
19 - 42
الكلمات الإفتتاحية
الملخص
في هذا البحث، نحن بصدد دراسة سلوك حلول المعادلات من الشكل (P) عندما الزمن t يؤول إلى المالانهاية، تحت بعض الشروط على دالة الذاكرة g والوسيطينm ,p . سنجد أن هناك تناقص على شكل أسي للطاقة (سلوك الحلول) عندما m=2 وتناقص على شكل كثير الحدود عندما m>2 بشرط أخذ المعطيات الابتدائية صغيرة ما أمكن.
Zennir, K. (2012). Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation. An-Najah University Journal for Research - A (Natural Sciences), 26(1), 19–42. https://doi.org/10.35552/anujr.a.26.1.95
[1]K. Zennir, “Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation,” An-Najah University Journal for Research - A (Natural Sciences), vol. 26, no. 1, pp. 19–42, Feb. 2012, doi: 10.35552/anujr.a.26.1.95.
Zennir, Khaled. “Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation.” An-Najah University Journal for Research - A (Natural Sciences), vol. 26, no. 1, Feb. 2012, pp. 19–42. Crossref, https://doi.org/10.35552/anujr.a.26.1.95.
1.Zennir K. Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2012 Feb;26(1):19–42. Available from: http://dx.doi.org/10.35552/anujr.a.26.1.95
Zennir, Khaled. “Decay of Solutions of a Nonlinear Viscoelastic Hyperbolic Equation.” An-Najah University Journal for Research - A (Natural Sciences) 26, no. 1 (February 2012): 19–42. https://doi.org/10.35552/anujr.a.26.1.95.
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