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Uniqueness and stability of solutions for Cauchy problem of nonlinear diffusion equations. (English) Zbl 0908.35052

The authors study the uniqueness and stability of BV-solutions for the Cauchy problem for the nonlinear diffusion equation \[ {\partial u\over\partial t}= \Delta A(u)+ \sum^N_{i= 1} {\partial b^i(u)\over\partial x_i}+ c(u) \] under the assumption that \(A(u)\) is strictly increasing.

MSC:

35K15 Initial value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations

Keywords:

BV-solutions
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References:

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