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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.

##### MSC:
 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