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Multidimensional traveling wavefronts in a model from combustion theory and in related problems. (English) Zbl 0786.35080
Summary: The paper deals with the flame propagation model \(\partial u/ \partial t=\Delta u+\beta(y)\partial u/ \partial x+f(u)\) in \(\Sigma=\{(x,y)\in \mathbb{R} \times \Omega\}\), \(\partial u/ \partial \nu=0\) at \(\partial \Sigma\), \(0=u(-\infty,\cdot)\leq u(x,\cdot)\leq u(\infty,\cdot)=1\) in \(\overline\Omega\) for all \(x \in \mathbb{R}\). Here \(\Omega \subset \mathbb{R}^{n- 1}\) is a bounded domain with a sufficiently smooth boundary, \(\nu\) is the unit outward normal to \(\partial \Sigma\), \(\beta:\Omega \to \mathbb{R}\) and \(f:[0,1]\to \mathbb{R}\) are sufficiently smooth and \(f(0)=f(1)=0\). Existence results concerning traveling wavefronts are given for that model and for related problems of practical interest.

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35K57 Reaction-diffusion equations
80A32 Chemically reacting flows
80A25 Combustion