51 research outputs found
Global existence of solutions of semilinear heat equation with nonlinear memory condition
We consider a semilinear parabolic equation with flux at the boundary
governed by a nonlinear memory. We give some conditions for this problem which
guarantee global existence of solutions as well as blow up in finite time of
all nontrivial solutions. The results depend on the behavior of variable
coefficients as $t \to \infty.
An explicit solution for a multimarginal mass transportation problem
We construct an explicit solution for the multimarginal transportation
problem on the unit cube with the cost function and
one-dimensional uniform projections. We show that the primal problem is
concentrated on a set with non-constant local dimension and admits many
solutions, whereas the solution to the corresponding dual problem is unique (up
to addition of constants).Comment: 31 pages, 4 figures. The paper was completely rewritten. Heuristic
considerations to find a solution of the primal problem added. Algorithm to
find the primal problem solution numerically added (arbitrary marginals). The
construction was generalized for a C(ln x + ln y + ln z), C is convex.
Measure on the triangle was found with the support singular with respect to
the Lebesgue measur
Blow-up problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition
In this paper we consider initial boundary value problem for nonlinear
nonlocal parabolic equation with absorption under nonlinear nonlocal boundary
condition and nonnegative initial datum. We prove comparison principle, global
existence and blow-up of solutions.Comment: arXiv admin note: text overlap with arXiv:1602.0501
Blow-up of solutions for a semilinear parabolic equation with nonlinear memory and absorption under nonlinear nonlocal boundary condition
In this paper we consider initial boundary value problem for a parabolic
equation with nonlinear memory and absorption under nonlinear nonlocal boundary
condition. We prove global existence and blow-up of solutions.Comment: arXiv admin note: substantial text overlap with arXiv:2208.0573
Local existence of solutions and comparison principle for initial boundary value problem with nonlocal boundary condition for a nonlinear parabolic equation with memory
We consider an initial value problem for a nonlinear parabolic equation with
memory under nonlinear nonlocal boundary condition. In this paper we study
classical solutions. We establish the existence of a local maximal solution. It
is shown that under some conditions a supersolution is not less than a
subsolution. We find conditions for the positiveness of solutions. As a
consequence of the positiveness of solutions and the comparison principle of
solutions, we prove the uniqueness theorem
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