Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions Article Swipe

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YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2212.09164

We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based on the study of the corresponding hyperbolic systems associated with the Riemann invariants. The key ingredient in the study of these systems is the use of the internal dissipation energy to estimate the difference of solutions with their mean values in an average sense.

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Mathematical Analysis

Mathematics

Dirichlet Distribution

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Mathematical analysis Dissipation Mathematics Space (punctuation) Exponential function Boundary value problem Dirichlet distribution Boundary (topology) Exponential decay Dirichlet boundary condition Wave equation Function (biology) Energy (signal processing) Physics Philosophy Thermodynamics Nuclear physics Evolutionary biology Biology Statistics Linguistics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2212.09164
PDF: https://arxiv.org/pdf/2212.09164
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DOI: https://doi.org/10.48550/arxiv.2212.09164

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Title: Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions

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Type: preprint

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Language: en

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Publication year: 2022

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Publication date: 2022-12-18

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Authors: Yacine Chitour, Hoài-Minh Nguyên

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Concepts: Mathematical analysis, Dissipation, Mathematics, Space (punctuation), Exponential function, Boundary value problem, Dirichlet distribution, Boundary (topology), Exponential decay, Dirichlet boundary condition, Wave equation, Function (biology), Energy (signal processing), Physics, Philosophy, Thermodynamics, Nuclear physics, Evolutionary biology, Biology, Statistics, Linguistics

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