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Zbl 1173.35557
Petitta, Francesco
A non-existence result for nonlinear parabolic equations with singular measures as data. (English)
[J] Proc. R. Soc. Edinb., Sect. A, Math. 139, No. 2, 381-392 (2009). ISSN 0308-2105; ISSN 1473-7124/e

Summary: We prove a non-existence result for nonlinear parabolic problems with zero lower-order terms whose model is $$\align u_t-\Delta_pu+|u|^{q-1}u &=\lambda \quad\text{in }(0,T)\times\Omega,\\ u(0,x)&=0\quad\text{in }\Omega,\\ u(t,x)&= 0\quad\text{on }(0,T)\times\partial\Omega, \endalign$$ where $\Delta_p= \text{div} (|\nabla u|^{p-2}\nabla u)$ is the usual $p$-Laplace operator, $\lambda$ is measure concentrated on a set of zero parabolic $r$-capacity $(1<p<r)$ and $q$ is large enough.

MSC 2000:: *35K60 (Nonlinear) BVP for (non)linear parabolic equations
35R05 PDE with discontinuous coefficients or data

Keywords: zero lower-order terms; $p$-Laplace operator

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Zentralblatt MATH Berlin [Germany]