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ABSTRACT In this short note, we discuss some results concerning the long-time behaviour of solutions to dissipative sine-Gordon equation in a bounded domain of . We first prove that without… Click to show full abstract
ABSTRACT In this short note, we discuss some results concerning the long-time behaviour of solutions to dissipative sine-Gordon equation in a bounded domain of . We first prove that without forcing term and under some assumptions on the domain then the global attractor reduces to . We then rewrite the sine-Gordon equation as a Schrödinger equation with smoothing; this allows us to provide another proof for the so-called asymptotical smoothing effect for this dissipative wave equation.
Keywords:
sine gordon;
equations remarks;
equation;
dissipative sine;
gordon equations;
remarks dissipative
Journal Title: Complex Variables and Elliptic Equations
Year Published: 2019
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Journal Title: Complex Variables and Elliptic Equations
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!