Transformation of approximate solutions of linear parabolic equations into asymptotic solutions of quasilinear parabolic equations
We present formulas that express the solution of the quasilinear equation \(z_\delta- \varepsilon(K(z) z_\xi)_\xi= 0\) in terms of the solution to the linear equation with variable coefficients \(u_t- \varepsilon \mu u_{xx}= C\), where \(\mu= \mu(x, t, \varepsilon)= \mu_0(x, t)+ \mu_1(x, t)+\cdots\) is a function to be determined. As a special case, the collection of formulas relate soutions of simple wave type (functions of arguments \(x+ bt\), \(b=\text{const}\)), quasilinear equations, and semilinear parabolic equations.
scientific article; zbMATH DE number 830777