Existence of a Solution to the Stefan Problem with Joule′s Heating

Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

“…From (17) it is easy to obtain the following system of (N − 1) linear algebraic equations: h 6 − τ h α n+1 j−1 + 2h 3 + τ 2h α n+1 j + h 6 − τ h α n+1 j+1 = h 6 α n j−1 + 2h 3 α n j + h 6 α n j+1…”

“…The time evolution model (1) describes the temperature profile of a thermistor device with electrical resistivity f , see [3,4,5,8,9,10,14,15,17,19]; the dimensionless parameter λ can be identified with the square of the applied potential difference V at the ends of the conductor. The system (1) has been the subject of a variety of investigations in the last decade.…”

Existence and uniqueness for the nonstationary problem of the electrical heating of a conductor due to the Joule‐Thomson effect

“…(s) _< ,s e R for some M _> m the existence of a weak solution is established for (1.1) in [2]. A result due to Shi, Shillor, and Xu [3] asserts that the assumption that N 2 and a cl(tt) in [2] can be eliminated.…”

“…However, in the generality considered here it does not seem likely that u can be bounded. Now we are ready to prove an existence assertion for the following problem: [3] using a discretization technique. Let k6 n E {1,2 }.…”

Semidiscretization for a nonlocal parabolic problem

“…Whereas, semidiscretization has been involved for the equations of the thermistor problem in [1,9]. Our aim here is to continue the study of problem (1.1) initiated in [6], where an a priori L ∞ -estimate is derived.…”