Gevrey Estimates of Formal Solutions for Certain Moment Partial Differential Equations with Variable Coefficients
Maria Suwińska
Abstract
Abstract The goal of this paper is to investigate Gevrey properties of formal solutions of certain generalized linear partial differential equations with variable coefficients. In particular, we extend the notion of moment partial differential equations to include differential operators that are not connected with kernel functions. Using the modified version of Nagumo norms and the properties of the Newton polygon we compute the Gevrey estimate for formal solutions of such generalized partial differential equations.
Topics & Concepts
MathematicsFirst-order partial differential equationStochastic partial differential equationPartial differential equationMathematical analysisVariable (mathematics)Numerical partial differential equationsMoment (physics)Kernel (algebra)Partial derivativeSeparable partial differential equationDifferential equationApplied mathematicsHyperbolic partial differential equationPolygon (computer graphics)Method of characteristicsDifferential (mechanical device)Constant coefficientsSymbol of a differential operatorElliptic partial differential equationLinear differential equationNewton polygonDistributed parameter systemParabolic partial differential equationExponential integratorNonlinear systemPolynomial and algebraic computationNonlinear Waves and SolitonsMathematical functions and polynomials