Existence and uniqueness of very singular solution of a degenerate parabolic equation with nonlinear convection.
Existence and uniqueness result for a class of nonlinear parabolic equations with L¹ data
We prove the existence and uniqueness of a renormalized solution for a class of nonlinear parabolic equations with no growth assumption on the nonlinearities.
Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains
In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence...
Existence and uniqueness results for solutions of nonlinear equations with right hand side in
We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here and the solution belongs to the so-called grand Sobolev space . This is the proper space when the right hand side is assumed to be only -integrable. In particular, we obtain the exponential integrability of the solution, which in the linear case was previously proved by Brezis-Merle and Chanillo-Li.
Existence and uniqueness results of positive solutions for nonvariational quasilinear elliptic systems.
Existence and uniqueness results on Single-Peaked solutions of a semilinear problem
Existence and Uniqueness Theorem for Singular Initial Value Problems and Applications
Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆
We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional...
Existence and upper semicontinuity of uniform attractors in for nonautonomous nonclassical diffusion equations
We prove the existence of uniform attractors in the space for the nonautonomous nonclassical diffusion equation , ε ∈ [0,1]. The upper semicontinuity of the uniform attractors at ε = 0 is also studied.
Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions
In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence,...
Existence by minimisation of solitary water waves on an ocean of infinite depth
Existence, comportement à l'infini et stabilité dans certains problèmes quasilinéaires elliptiques et paraboliques d'ordre 2
Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée
Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée
Existence de lois de conservation dans le cas cyclique
Existence de maillages optimaux dans les méthodes d'éléments finis
Existence de nappes de tourbillon pour l'équation d'Euler sur le plan
Existence de solutions avec petite donnée initiale dans pour une équation de Dirac non linéaire
Existence de solutions faibles pour un modèle d'écoulement triphasique en milieu poreux
Existence de solutions non bornées pour certaines équations quasi-linéaires