On the construction of approximate solutions for a multidimensional nonlinear heat equation. (English) Zbl 0837.35065

Summary: We study three methods, based on continuous symmetries, to find approximate solutions for the multidimensional nonlinear heat equation \(\partial u/\partial x_0+ \Delta u= au^n+ \varepsilon f(u)\), where \(a\) and \(n\) are arbitrary real constants, \(f\) is a smooth function, and \(0< \varepsilon\ll 1\).


35K55 Nonlinear parabolic equations
35A35 Theoretical approximation in context of PDEs
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