| Summary: | In this work, we consider a class of initial boundary value problems for fourth-order dispersive wave equations with superlinear damping and non-local source terms as well as time-dependent coefficients in <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>Ω</mo><mo>×</mo><mo>(</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>Ω</mo></semantics></math></inline-formula> is a bounded domain in <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></semantics></math></inline-formula> and <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>. We prove that there exists a safe time interval of existence in the solution <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></semantics></math></inline-formula>, with <i>T</i> being a lower bound of the blowup time <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>t</mi><mo>*</mo></msup></semantics></math></inline-formula>. Moreover, we find an explicit lower bound of <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>t</mi><mo>*</mo></msup></semantics></math></inline-formula>, assuming the coefficients are positive constants.
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