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OALib Journal期刊
ISSN: 2333-9721
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On the dimension of the kernel of the linearized thermistor operator

Keywords: Elliptic system , thermistor problem , existence , uniqueness of solutions

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Abstract:

The elliptic system of partial differential equations of the thermistor problem is linearized to obtain the system $$displaylines{ ablacdot(sigma(ar u) ablaPhi+sigma'(ar u)U ablaarvarphi)=0 quad ext{in }Omega,quad Phi=0quadhbox{on }Gammacr Delta U+sigma'(ar u)| ablaarvarphi|^2 U+2sigma(ar u) ablaar varphi cdot ablaPhi=0quad hbox{in }Omega, quad U=0quadhbox{on } Gamma. }$$ We study the existence of nontrivial solutions for this linear boundary-value problem, which is useful in the study of the thermistor problem.

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