Existence of pseudo almost automorphic solutions for the heat equation with -pseudo almost automorphic coefficients.
Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities
We study the problem ∂b(x,u)/∂t - div(a(x,t,u,Du)) + H(x,t,u,Du) = μ in Q = Ω×(0,T), in Ω, u = 0 in ∂Ω × (0,T). The main contribution of our work is to prove the existence of a renormalized solution without the sign condition or the coercivity condition on H(x,t,u,Du). The critical growth condition on H is only with respect to Du and not with respect to u. The datum μ is assumed to be in and b(x,u₀) ∈ L¹(Ω).
Existence of solution to transpiration control problem.
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 quasilinear parabolic equations with nonlocal boundary conditions.
Existence of the Displacements Field for an Elasto-Plastic Body Subject to Hencky's Law and von Mises Yield Condition.
Existence of weak solutions to doubly degenerate diffusion equations
We prove existence of weak solutions to doubly degenerate diffusion equations by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains with Dirichlet or Neumann boundary conditions. The function can be an inhomogeneity or a nonlinearity involving terms of the form or . In the appendix, an introduction to weak differentiability...
Existence result for variational degenerated parabolic problems via pseudo-monotonicity.
Existence results for a class of nonlinear parabolic equations in Orlicz spaces.
Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations.
Existenzsätze mit der Linienmethode für Parabolische Probleme und periodische Lösungen von ut = f(t,x,u,ux,uxx).
Explicit exponential decay bounds in quasilinear parabolic problems.
Explicit inequalities for parabolic and pseudoparabolic equations with Neumann boundary conditions.
Exponential decay of a solution for some parabolic equation involving a time nonlocal term
We consider the large time behavior of a solution of a parabolic type equation involving a nonlocal term depending on the unknown function. This equation is proposed as a mathematical model of carbon dioxide transport in concrete carbonation process, and we proved the existence, uniqueness and large time behavior of a solution of this model. In this paper, we derive the exponential decay estimate of the solution of this model under restricted boundary data and initial data.
Extinction and non-extinction of solutions for a nonlocal reaction-diffusion problem.
Extinction for fast diffusion equations with nonlinear sources.
Extremal Solutions for Nonlinear Parabolic Problems with Discontinuities.