Global Attractor for a Class of Parabolic Equations with Infinite Delay
We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.
Global attractors for two-phase Stefan problems in one-dimensional space.
Global branching for discontinuous problems
Global existence for functional semilinear integro-differential equations
In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps.
Global existence for the conserved phase field model with memory and quadratic nonlinearity.
Global existence for the discrete diffusive coagulation-fragmentation equations in L1.
Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid
Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.
Global existence, uniqueness, and continuous dependence for a reaction-diffusion equation with memory.
Global free boundary problem for incompressible magnetohydrodynamics [Book]
Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field.
Global inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation of second order
Global solutions and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary.
Global solvability of the mixed problem for first order functional partial differential equations
Global superconvergence of finite element methods for parabolic inverse problems
In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.
Global uniqueness for an inverse boundary problem arising in elasticity.
Global uniqueness results for fractional order partial hyperbolic functional differential equations.
Global uniqueness results for fractional partial hyperbolic differential equations with state-dependent delay
We investigate the existence and uniqueness of solutions of hyperbolic fractional order differential equations with state-dependent delay by using a nonlinear alternative of Leray-Schauder type due to Frigon and Granas for contraction maps on Fréchet spaces.
Global well-posedness and blow up for the nonlinear fractional beam equations
We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.
Gradient potential estimates
Pointwise gradient bounds via Riesz potentials like those available for the Poisson equation actually hold for general quasilinear equations.
Gradient theory for plasticity via homogenization of discrete dislocations
We deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal under study, so that the mathematical formulation will involve a two-dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so-called core region. We show that the -limit of this energy (suitably rescaled),...