Existence and non-existence results for a nonlinear heat equation.
Existence and nonexistence results for reaction-diffusion equations in product of cones
Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.
Existence and regularity for semilinear parabolic evolution equations
Existence and regularity of optimal solution for a dead oil isotherm problem.
Existence and stability of asymptotically oscillatory double pulses.
Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face.
Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems
A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.
Existence and uniqueness of periodic solutions for a nonlinear reaction-diffusion problem.
We consider a class of degenerate reaction-diffusion equations on a bounded domain with nonlinear flux on the boundary. These problems arise in the mathematical modelling of flow through porous media. We prove, under appropriate hypothesis, the existence and uniqueness of the nonnegative weak periodic solution. To establish our result, we use the Schauder fixed point theorem and some regularizing arguments.
Existence and uniqueness of solutions Cauchy problem for nonlinear infinite systems of parabolic differential-functional equations.
Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations
We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.
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 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, 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 of a solution for a class of nonlinear parabolic systems.
Existence of a solution for the initial boundary value problem for a high order parabolic equation in an unbounded domain.
Existence of a solution of a Fourier nonlocal quasilinear parabolic problem.
Existence of extremal periodic solutions for nonlinear evolution inclusions
We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.
Existence of global solution for a differential system with initial data in .
Existence of global solution for a nonlocal parabolic problem.