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.
Existence of global solutions for systems of reaction-diffusion equations on unbounded domains.
Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in .
Existence of periodic solutions for a class of nonlinear evolution equations.
Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.
Existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions and its applications
We establish the existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions. The energies associated to these evolution equations are quadratic forms. Our approach is based on application of the Schaefer fixed-point theorem combined with the continuity method.
Existence of solutions for infinite systems of parabolic equations with functional dependence
The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method.
Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions
The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet -Laplace operator.
Existence of solutions for nonlinear parabolic problems
We consider nonlinear parabolic boundary value problems. First we assume that the right hand side term is discontinuous and nonmonotone and in order to have an existence theory we pass to a multivalued version by filling in the gaps at the discontinuity points. Assuming the existence of an upper solution and of a lower solution such that , and using the theory of nonlinear operators of monotone type, we show that there exists a solution and that the set of all such solutions is compact in...