The approximation of solutions to the backwards heat equation in a nonhomogeneous medium

DOI10.1016/0022-247X(79)90238-5zbMath0425.35061OpenAlexW2066176170MaRDI QIDQ1135442

David Colton

Publication date: 1979

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(79)90238-5

zbMATH Keywords

asymptotic estimatesquasireversibilityapproximation of solutionspseudoparabolic equationsbackwards heat equation in a nonhomogeneous mediumcomplete family of solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Heat equation (35K05) Ill-posed problems for PDEs (35R25) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70)

Related Items (7)

Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations ⋮ Shannon-Taylor technique for solving one-dimensional inverse heat conduction problem ⋮ Reconstructing an unknown time-dependent function in the boundary conditions of a parabolic PDE ⋮ A numerical method for identifying heat transfer coefficient ⋮ A procedure for determining a spacewise dependent heat source and the initial temperature ⋮ Simultaneous reconstruction of space-dependent heat transfer coefficients and initial temperature ⋮ A method for identifying a spacewise-dependent heat source under stochastic noise interference

Cites Work

• On an analogue of the Euler-Cauchy polygon method for the numerical solution of \(u_{xy}=f(x, y, u, u_x, u_y)\)
• Asymptotic behaviour of the fundamental solution to the equation of heat conduction in two temperatures
• The Approximation of Certain Parabolic Equations Backward in Time by Sobolev Equations
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