A necessary and sufficient condition for global existence for a quasilinear reaction-diffusion system.
A Neumann problem for a convection-diffusion equation on the half-line
We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.
A new approach to initial traces in nonlinear filtration
A new approach to solving a quasilinear boundary value problem with -Laplacian using optimization
We present a novel approach to solving a specific type of quasilinear boundary value problem with -Laplacian that can be considered an alternative to the classic approach based on the mountain pass theorem. We introduce a new way of proving the existence of nontrivial weak solutions. We show that the nontrivial solutions of the problem are related to critical points of a certain functional different from the energy functional, and some solutions correspond to its minimum. This idea is new even...
A new method to obtain decay rate estimates for dissipative systems
A new method to obtain decay rate estimates for dissipative systems with localized damping.
We consider the wave equation damped with a locally distributed nonlinear dissipation. We improve several earlier results of E. Zuazua and of M. Nakao in two directions: first, using the piecewise multiplier method introduced by K. Liu, we weaken the usual geometrical conditions on the localization of the damping. Then thanks to some new nonlinear integral inequalities, we eliminate the usual assumption on the polynomial growth of the feedback in zero and we show that the energy of the system decays...
A new method to obtain decay rate estimates for dissipative systems
We consider the wave equation damped with a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function ρ has not a polynomial behavior in zero. This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction...
A new partial regularity proof for solutions of nonlinear elliptic systems.
A new proof for a Rolewicz's type theorem: An evolution semigroup approach.
A new proof of Harnack's inequality for elliptic partial differential equations in divergence form.
A new type of solutions for a singularly perturbed elliptic Neumann problem.
A nonexistence result for a nonlinear equation involving critical Sobolev exponent
A nonexistence result for Yamabe type problems on thin annuli
A nonexistence test for biharmonic Green's functions of clamped bodies.
A nonexistence theorem for an equation with critical Sobolev exponent in the half space.
A nonlinear degenerate parabolic equation
A nonlinear elliptic boundary value problem
A nonlinear heat equation with temperature-dependent parameters.
A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation
A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions