Performance management and Problem Management

scope of these two management process

Answer:
ITIL (or ISO 20000) do not explicitly define Performance Management as a stand alone process. It's rather in scope of the Capacity Management or Continual Service Improvement. Performance management is about measuring, monitoring and improving (or fine tuning) performance of the service or component (or could be of your e.g. Service desk).
More details about Capacity Management could be found in the articles:
"ITIL and ISO 20000 – How to setup the Capacity Management process" https://advisera.com/20000academy/blog/2016/02/16/itil-and-iso-20000-how-to-setup-the-capacity-management-process/
"Three faces of Capacity Management" https://advisera.com/20000academy/knowledgebase/three-faces-capacity-management/
"ITIL Reactive and Proactive Capacity Management" https://advisera.com/20000academy/blog/2015/04/07/itil-reactive-and-proactive-capacity-management/

Problem Management has to find root cause of one or more incidents. An incident can have root cause in performance so from that point of view Problem Management can deal with performance as well. But Problem Management has much broader scope. This articles should explain:
"How to resolve the problem ticket/record according to ITIL/ISO 20000" https://advisera.com/20000academy/blog/2016/04/05/how-to-resolve-the-problem-ticketrecord-according-to-itiliso-20000/
"ITIL Reactive and Proactive Problem Management: Two sides of the same coin" https://advisera.com/20000academy/knowledgebase/itil-reactive-proactive-problem-management-two-sides-coin/
"ITIL and ISO 20000 Problem Management – Organizing for problem resolution" https://advisera.com/20000academy/blog/2014/07/29/itil-iso-20000-problem-management-organizing-problem-resolution/
"ITIL Problem Management: getting rid of problems" https://advisera.com/20000academy/blog/2013/08/05/itil-problem-management-getting-rid-problems/