-estimate for qualitatively bounded weak solutions of nonlinear degenerate diagonal parabolic systems.
-estimate for solutions of nonlinear parabolic systems
We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The -estimates are obtained by the Di Benedetto methods.
-estimates for nonlinear parabolic equations with natural growth conditions
-estimates for solutions of nonlinear parabolic systems with gradient linear growth
Existence of weak solutions and an -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.
Laplace asymptotics for generalized K.P.P. equation
Consider a one dimensional nonlinear reaction-diffusion equation (KPP equation) with non-homogeneous second order term, discontinuous initial condition and small parameter. For points ahead of the Freidlin-KPP front, the solution tends to 0 and we obtain sharp asymptotics (i.e. non logarithmic). Our study follows the work of Ben Arous and Rouault who solved this problem in the homogeneous case. Our proof is probabilistic, and is based on the Feynman-Kac formula and the large deviation principle...
Laplace asymptotics for generalized K.P.P. equation
Large solutions, metasolutions, and asymptotic behaviour of the regular positive solutions of sublinear parabolic problems.
Local exact controllability of the diffusion equation in one dimension.
Local exact lagrangian controllability of the Burgers viscous equation
Local Existence and Regularity for a Class of Degenerate Parabolic Equations.
Local solution for the Kadomtsev-Petviashvili equation with periodic conditions.
Local solvability of diagonal semilinear parabolic systems
Long-time behavior for a regularized scalar conservation law in the absence of genuine nonlinearity
Long-time vanishing properties of solutions of some semilinear parabolic equations