Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations
Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.
Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary.
Existence and uniqueness for a nonlinear dispersive equation.
Existence and uniqueness for a -Laplacian nonlinear eigenvalue problem.
Existence and uniqueness for magnetohydrodynamic flows in pipes with viscosity dependent on the temperature.
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 nonstationary problem of the electrical heating of a conductor due to the Joule-Thomson effect.
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 a classical solution of Fourier's first problem for nonlinear parabolic-elliptic systems.
Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
Existence and uniqueness of classical solutions to certain nonlinear integro-differential Fokker-Planck type equations.
Existence and uniqueness of classical solutions to second-order quasilinear elliptic equations.
Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data
Existence and uniqueness of generalized solutions to a telegraph equation with an integral boundary condition via Galerkin's method.
Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects.
Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
Existence and uniqueness of periodic solutions for a model of contaminant flow in porous medium.
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 pseudo almost automorphic mild solutions to some classes of partial hyperbolic evolution equations.