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

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.

Show me the PDF file (280 KB), TEX file for this article.

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

Return to the EJDE web page