On blow-up solutions and dead zones in semilinear equations
DOI:
https://doi.org/10.15407/dopovidi2018.04.009Keywords:
blowup solutions, quasiconformal mappings, semilinear PDEAbstract
Presented by Corresponding Member of the NAS of Ukraine V.Ya. Gutlyanskii We study semilinear elliptic equations of the form div(A(z)∇u)=f(u) in Ω⊂C, where A(z) stands for a sym metric 2×2 matrix function with measurable entries, detA=1, and such that 1/K|ξ|2⩽⟨A(z)ξ,ξ⟩⩽K|ξ|2,ξ∈R2,1⩽K<∞. Making use of our Factorization theorem, we give some explicit solutions for the above equation if f=eu or f=uq, when matrices A(z) are chosen in an appropriate form.
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