Cauchy problems for evolutionary pseudodifferential equations over \(p\)-adic field (Q1724238)

Summary: We study a class of evolutionary pseudodifferential equations of the second order in \(t\), \((\partial^2 u(t,x)/\partial t^2+2a^2 T^{\alpha/2}(\partial u(t,x)/\partial t)+b^2 T^\alpha u(t,x)+c^2u (t,x)=q(t,x))\), where \(t\in (0,z]\) and \(T^\alpha\) is pseudodifferential operator in \(x\in Q_p\), which defined by \textit{W. Su} [Sci. China, Ser. A 35, No. 7, 826--836 (1992; Zbl 0774.43006)]. We obtain the exact solutions to the equations which belong to mixed classes of real and \(p\)-adic functions.