Tent space well-posedness for parabolic Cauchy problems with rough coefficients

Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C 0 (β,γ) (E α-β ) of all E α-β -valued continuous functions φ(t) on [0, T] satisfying a Höld...

Well-posedness for Hyperbolic Problems

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

Existence of Solutions for Degenerate Parabolic Equations with Rough Coefficients

We prove that a sequence of quasi-solutions to non-degenerate degenerate parabolic equations with rough coefficients is strongly Lloc-precompact. The result is obtained using the H-measures and a new concept of quasihomogeneity. A consequence of the precompactness is existence of a weak solution to the equation under consideration.

Well-posedness of parabolic equations containing hysteresis with diffusive thresholds

In the paper, we develop a theory of reaction-diffusion equations containing discontinuous hysteresis operator — the so-called non-ideal relay. The nonideal relay (or a bi-stable relay, or lazy switch) is the most basic, yet nontrivial hysteresis operator. The state (output) of the non-ideal relay switches from −1 to 1 when the input exceeds a threshold value x ∈ R and switches back to state −1...