Electron. J. Differential Equations, Vol. 2016 (2016), No. 327, pp. 1-12.

Nonlinear parabolic equations with blowing-up coefficients with respect to the unknown and with soft measure data

Khaled Zaki, Hicham Redwane

Abstract:
We establish the existence of solutions for the nonlinear parabolic problem with Dirichlet homogeneous boundary conditions,
$$ \frac{\partial u}{\partial t} - \sum_{i=1}^N\frac{\partial}{\partial x_i} \Big( d_i(u)\frac{\partial u}{\partial x_i} \Big) =\mu,\quad u(t=0)=u_0, $$
in a bounded domain. The coefficients $d_i(s)$ are continuous on an interval $]-\infty,m[$, there exists an index p such that $d_p(u)$ blows up at a finite value m of the unknown u, and $\mu$ is a diffuse measure.

Submitted September 9, 2016. Published December 22, 2016.
Math Subject Classifications: 47A15, 46A32, 47D20.
Key Words: Nonlinear parabolic equations; blowing-up coefficients; renormalized solutions; soft measure.

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Khaled Zaki
Faculté des Sciences et Techniques
Université Hassan 1, B.P. 764
Settat, Morocco
email: zakikhaled74@hotmail.com
Hicham Redwane
Faculté des Sciences Juridiques, Économiques et Sociales
Université Hassan 1, B.P. 764
Settat, Morocco
email: redwane_hicham@yahoo.fr

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