Existence of weak solutions with different initial energy levels to an equation modeling shallow-water waves

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Taşkesen H., Polat N.

International Journal of Open Problems in Computer Science and Mathematics, vol.14, no.4, pp.29-47, 2021 (Peer-Reviewed Journal)


The present paper considers the Cauchy problem of a generalized shallow water wave equation with two different initial energy levels. We investigate the existence of global weak solutions in critical and supercritical energy levels by sign preserving property of some functionals introduced for the potential well method.