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Estimates for viscosity solutions of parabolic equations with Dirichlet boundary conditions. (English) Zbl 1090.35097

Summary: It is shown how one can get upper bounds for \(| u-v |\) when \(u\) and \(v\) are the (viscosity) solutions of \[ u_t - \alpha(D_x u) \Delta_x u = 0 \text{ and } v_t - \beta(D_x v) \Delta_x v = 0, \] respectively, in \((0,\infty)\times \Omega\) with Dirichlet boundary conditions. Similar results are obtained for some other parabolic equations as well, including certain equations in divergence form.

MSC:

35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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