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Wave breaking for the periodic weakly dissipative Dullin-Gottwald-Holm equation. (English) Zbl 1202.37109
Summary: We consider the periodic weakly dissipative Dullin-Gottwald-Holm equation. The present work is mainly concerned with blow-up phenomena for the Cauchy problem for this new kind of equation. We apply the optimal constant to give sufficient conditions via an appropriate integral form of the initial data, which guarantees a finite-time singularity formation for the corresponding solution.
MSC:
37L05General theory, nonlinear semigroups, evolution equations
35C05Solutions of PDE in closed form
26A12Rate of growth of functions of one real variable, orders of infinity, slowly varying functions
58E35Variational inequalities (global problems)
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