Magnetic field caused by electric field A sudden change in electric field will cause just magnetic field or changing magnetic field ?
Once the electric field is established and is not changing then what will happen to the magnetic field which was caused by the changing electric field? 
Will the magnetic field (which was caused by the changing electric field) remains constant or will collapse ? 
 A: Assuming that there are no currents, the divergence and curl of the magnetic field satisfy Maxwell's equations:
$$\boldsymbol{\nabla} \cdot \mathbf B(\mathbf x,t) = 0,$$
$$\boldsymbol{\nabla} \times \mathbf B(\mathbf x,t) = \frac{1}{c^2} \frac{\partial \mathbf{E}(\mathbf x,t)}{\partial t}.$$
Assuming that the time-dependence of the total electric field is known, the formal solution to this (along with the condition that $\mathbf E, \mathbf B \rightarrow 0$ at infinity) is
$$\mathbf{B}(\mathbf x,t) = \frac{1}{4 \pi c^2} \int_{\mathbb R^3} d^3\mathbf x' \ \frac{\partial \mathbf{E}(\mathbf x',t)}{\partial t} \times \frac{\mathbf x - \mathbf x'}{|\mathbf x - \mathbf x'|^3}.$$
This can be derived by analogy with the Biot-Savart law, since the current density $\mathbf J$ is simply replaced by $\epsilon_0 \partial \mathbf E/\partial t$ in the curl equation.
Do note however that $\mathbf E(\mathbf x,t)$ written here is the net electric field, which is not necessarily the applied field; the time-changing magnetic field itself creates an electric field that is included in $\mathbf E$ in the above expression.
You can see from this equation that in general, a time-dependent electric field can create a time-dependent magnetic field, which dies down after the electric field has settled on a constant value (i.e. $\partial \mathbf E/\partial t \sim 0$).
A: A changing electric field causes a magnetic field and vice versa. This is given by the two Maxwell's equations.
$$\mathbf E\cdot  d\mathbf l=-\dfrac{d\phi_B}{dt}$$
This is the well known Faraday's law and states that a changing magnetic field creates an electric field (or induces an EMF). 
This induced electric field will be constant as long as the time derivative of magnetic flux is constant.
Now we have another equation which discusses the induction of a magnetic field with a changing electric field. This equation is also known as the Ampere-Maxwell equation.
$$\mathbf B\cdot d\mathbf l=\mu_0\epsilon_0\dfrac{d\phi_E}{dt}+\mu_0I$$
Let's assume the term $\mu_0I$ to be zero for a while because that only matters when there is a current moving through a wire, then we're just left with 
$$\mathbf B\cdot d\mathbf l=\mu_0\epsilon_0\dfrac{d\phi_E}{dt}$$
which is the displacement current term and will be non-zero in case of a changing electric field. It simply ensures continuity of the magnetic field like in the case of a charging-discharging capacitor connected to an AC supply.
It works in the same manner as the previous one. 
That means, if the rate of change of electric field is constant, the magnetic field thus produced will also be constant.

Once the electric field is established and is not changing then what will happen to the magnetic field which was caused by the changing electric field? 

We should notice that in both the cases, once the change stops i.e. the derivative becomes $0$ the left hand side of the equation also goes to $0$. So yes, if the change stops, the generation of the other field is also stopped.

Will the magnetic field (which was caused by the changing electric field) remain constant or collapse? 

It will remain constant as long as $\dfrac{d\phi_E}{dt}$ is constant. But as you slow down and finally stop changing the electric field, the magnetic field will collapse as in the case of a DC capacitor circuit after a very long time when the current goes to $0$.
