Solvability of the first boundary value problem for the heat-conduction equation with nonlinear sources and strong power singularities

DOI10.1007/S11253-014-0877-ZzbMath1327.35205OpenAlexW2033982258MaRDI QIDQ2259460

O. Yu. Chmyr

Publication date: 4 March 2015

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-014-0877-z

zbMATH Keywords

heat equationexistence of solutionscontraction principleSchauder fixed point theoremnonlinear point sourcespoint power singularities

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Cites Work

• Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition
• The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions
• Parabolic problems with nonlinear boundary conditions and critical nonlinearities
• On critical exponents for the heat equation with a mixed nonlinear Dirichlet-Neumann boundary condition
• Existence and nonexistence of global solutions of quasilinear parabolic equations.
• On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary
• Composition of parabolic kernels
• On solution of the parabolic boundary value problem with strong power singularities on the right side
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