Abstract
The discontinuous boundary value problem of steady state temperatures in a quarter plane gives rise to a pair of dual integral equations which are not of Titchmarch type. These dual integral equations are considered in this paper.
Highlights
We consider the problem of steady state temperatures in a quarter plane, whose edge x 0 is losing heat to environment at zero temperature according to Newton’s Law of cooling while on the edge y 0, temperature is controlled on portion of this edge, while the heat input is known on the remaining part
The discontinuous boundary value problem of steady state temperatures in a quarter plane gives rise to a pair of dual integral equations which are not of Titchmarch type
These dual integral equations are considered in this paper
Summary
We consider the problem of steady state temperatures in a quarter plane (seeFig. 1), whose edge x 0 is losing heat to environment at zero temperature according to Newton’s Law of cooling while on the edge y 0, temperature is controlled on portion of this edge, while the heat input is known on the remaining part. The discontinuous boundary value problem of steady state temperatures in a quarter plane gives rise to a pair of dual integral equations which are not of Titchmarch type. These dual integral equations are considered in this paper. We propose to solve such dual integral equations for the function f(t) in this paper.
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