Initial Value Problem for Max Equations with an External Parameter and Systems of Max Equations

Abstract

Abstract. We consider the initial value problem for the evolution equations defined by max operators. Though the complexity of expression of general solutions is usually of exponential order, there exist some equations of which order can be reduced to polynomial one using simplification of solution expression. We consider importing an external parameter to the max equations or constructing a system of the max equations. Some concrete examples are reported of which order of solution complexity can be preserved as polynomial.