Parabolic Boundary-Value Problems

C. V. Pao
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C. V. Pao: North Carolina State University

Chapter Chapter 2 in Nonlinear Parabolic and Elliptic Equations, 1992, pp 47-92 from Springer

Abstract: Abstract The use of upper and lower solutions as initial iterations, discussed in the previous chapter, leads to two monotone sequences each of which converges to a unique solution of an integral equation. This chapter shows that the limit of the monotone sequence is indeed the solution of the parabolic problem for each of the three basic boundary conditions. This regularity result is given in the framework of a more general parabolic boundary-value problem using the property of a fundamental solution. The same approach is extended to a class of integroparabolic equations of Volterra and Fredholm types. It is also extended to a parabolic boundary-value problem with time delay in the reaction function. Some qualitative properties of the solution such as positivity and boundedness are also included in the discussion.

Keywords: Lipschitz Condition; Lower Sequence; Monotone Property; Lower Solution; Reaction Function (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-3034-3_2

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DOI: 10.1007/978-1-4615-3034-3_2

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