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We study the following wave equation $$u_{tt}-\Delta u+\alpha (t)\left| u_{t}\right| ^{m(\cdot )-2}u_{t}=0$$ with a nonlinear damping having a variable exponent m(x) and a time-dependent coefficient $$\alpha (t)$$ . We use… Click to show full abstract
We study the following wave equation $$u_{tt}-\Delta u+\alpha (t)\left| u_{t}\right| ^{m(\cdot )-2}u_{t}=0$$ with a nonlinear damping having a variable exponent m(x) and a time-dependent coefficient $$\alpha (t)$$ . We use the multiplier method to establish energy decay results depending on both m and $$\alpha $$ . We also give four numerical tests to illustrate our theoretical results using the conservative Lax–Wendroff method scheme.
Keywords:
time dependent;
exponent time;
wave equation;
nonlinear damping;
variable exponent
Journal Title: Arabian Journal of Mathematics
Year Published: 2021
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Journal Title: Arabian Journal of Mathematics
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!