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Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations. (English) Zbl 1167.35418

Summary: We study the Cauchy problem of a class of multidimensional generalized double dispersion equations \(u_{tt} - \Delta u - \Delta u - tt+\Delta ^{2}u+k\Delta u_t=\Delta f(u)\). We prove the global existence of weak solution under some assumptions on the nonlinear term and the initial data.

MSC:

35L75 Higher-order nonlinear hyperbolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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