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Finding of Exact Solution to Nonlinear Operator Equation

Authors: Agapov O.A. Published: 17.10.2013
Published in issue: #4(39)/2010  
DOI:

 
Category: Mathematics and Mechanics  
Keywords: operator equations, differential equations, nonlinear differential equations, partial differential equations

The exact solution is found for the nonlinear operator equation of the form du(r,t)/dt = A[u(r,t)], u : Rn x R+ → R under condition u(r, 0) = φ(r) for operator A infinitely differentiable by Frechet. Examples of solving the Cauchy problems for equations of heat conduction, advection, ordinary differential equation with separable variables, and the Corteweg-de Fries equation.